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Notes: This paper reports observations of rapid energy transport effects resulting from high intensity laser heating of fused silica targets. Picosecond optical probing of these interactions provides information on the kinematics of supersonic ionization fronts driven into the targets. Studies have been conducted as a function of laser intensity, wavelength, and target angle. Additionally, targets with metallic surface layers have been investigated. Characterization of the laser absorption has enabled plasma and radiation hydrodynamics energy transport simulations to be implemented. Although consideration has been given to several energy transport mechanisms, including thermal and suprathermal electron transport, the kinematics are best explained with a radiation transport model. This is confirmed by angled and high and medium Z coated target experiments. © 1998 American Institute of Physics.

Notes: A Saturn accelerator study of annular, aluminum-wire-array, Z-pinch implosions in the calculated high-wire-number plasma-shell regime [Phys. Rev. Lett. 77, 5063 (1996)] shows that a factor of 2 decrease in pulse width and an associated doubling of the total radiated x-ray power occurs when the mass of 12 mm radius, 2 cm long array is reduced from above 1.9 mg to below 1.3 mg. The study utilized extensive time- and space-resolved measurements to characterize the implosion over the mass range 0.42–3.4 mg. Eulerian radiation-magnetohydrodynamic-code simulations in the r-z plane agree qualitatively with the measurements. They suggest that the pulse-width decrease with mass is due to the faster implosion velocity of the plasma shell relative to the growth of the shell thickness that arises from a two-stage development of the magnetic Rayleigh–Taylor instability. Over the bulk of the mass-range explored, the variation in K-shell (lines plus free-bound continuum) yield is in qualitative agreement with simple K-shell radiation-scaling models. These models indicate that the doubling of the measured K-shell yield, which also occurs for masses below 1.3 mg relative to masses above 1.9 mg, arises from increased plasma temperature. © 1998 American Institute of Physics.

Notes: A rigorous form of Langevin equation for the particle-in-cell simulation of a collisional plasma is obtained. The method is checked by reproducing the known results on the simulation of the electron runaway in a fully ionized uniform plasma with Maxwellian collisions. The non-Maxwellian effect owing to the electron heat flow on the runaway is explored. © 1998 American Institute of Physics.

Notes: Intermittent chaotic phenomena caused by the current-driven ion acoustic instability are experimentally observed using a Double Plasma device, in which two mesh grids are installed to excite the instability. When a dc potential is applied to one of the two mesh grids and exceeds a certain threshold, the system suddenly transits from a periodic state to a chaotic state. At the same time, the signals picked up as perturbation components of a current exhibit intermittent turbulent bursts. The calculations of the correlation dimension and the Lyapunov exponent indicate that the system reaches a chaotic state. Furthermore, it is found that the results of mathematical and statistical analysis of observed signals agree with the theoretical properties of the type-1 intermittency: the occurrence of 1/f-type low-frequency noise and the probability distribution of the duration between two bursts. Therefore, it is concluded that the present system reaches a chaotic state via the type-1 intermittency. © 1998 American Institute of Physics.

Notes: Plasma screening effects on photoionizations from the 1s state of hydrogenic ions in dense weakly plasmas are investigated. The particle interaction potential in weakly coupled plasmas is obtained by the static Debye-Hückel model. The initial bound wave function and energy eigenvalue of the target ion are modified in the Debye-Hückel potential using the Ritz variation method. The final state of the ejected photoelectron is represented by a plane wave solution. The Coulomb correction is considered using the screened Coulomb wave function. The photoionization cross section is obtained the acceleration form of the matrix element in order to investigate the plasma screening effects on the interaction potential. The screening effect is obtained as a function of the Debye length and photon energy. The retardation correction effect is also considered in obtaining the total 1s photoionization cross section in plasmas. The plasma screening effects on the photoionization cross section for the interesting domain of the Debye length, Λ≥10aZ, are found to be less than 10%. It is also found that the plasma screening effect is almost independent of the incident photon energy. © 1998 American Institute of Physics.

Notes: The poloidal magnetic field was measured to detect the plasma boundary position. It was found that the pressure-induced plasma shift, an observable characteristic of the Pfirsch–Schlüter current, depends strongly on the initial position of the magnetic axis. When the axis was moved by the vertical field inside the torus, the finite-β shift became smaller. Complete suppression of the finite-β plasma shift was achieved in a deeply inward shifted configuration: 7 cm from the standard position Raxis=2.20 m. This effect is explained by magnetohydrodynamic (MHD) equilibrium theory for stellarator toroidal plasmas with a large magnetic hill and deep inward shift. © 1998 American Institute of Physics.

Notes: A self-similar solution of the gas dynamics equations with heat conduction, which describes homologous contraction and expansion of gaseous masses with a free external boundary, is investigated in detail. As a primary application, implosion of deuterium–tritium (DT) fuel in inertial confinement fusion targets is considered. For strongly non-adiabatic implosions the self-similar solution predicts that the flow pattern should approach an asymptotical regime in which it ceases to depend on the initial entropy. For DT masses relevant to inertial confinement fusion (ICF) this regime begins to dominate at αUim(approximately-greater-than)6×108 cm/s, where α=p/pdeg is the fuel isentrope parameter, and Uim is its implosion velocity. The solution has also a branch which describes an asymptotical regime of explosive expansion after an ultra-fast initial heating to a strongly radiating state. © 1998 American Institute of Physics.

Notes: Brillouin enhanced four-wave mixing and phase conjugation of electromagnetic waves in weakly collisional fully ionized plasmas are considered. It is found that the nonlinearity associated with the nonlocal electron heat transport may dominate over the ponderomotive force and consequently there might appear an enhanced degenerate four-wave mixing and phase conjugation reflectivity. © 1998 American Institute of Physics.

Notes: A one-dimensional particle-in-cell simulation with Monte-Carlo collisions (PIC-MCC) has been used to study the breakdown, evolution and decay of a capacitive, radiofrequency (rf) argon discharge with parallel plate electrodes. The simulation uses spherical discharge geometry in order to represent a system with different area electrodes. Simple analytic and semi-analytic expressions have been determined to describe the temporal development of the average electron energy and the plasma density during these non-equilibrium periods. The expressions give quantities which are averaged over space and the rf cycle, and the results are compared with the simulated conditions. This simple model can be used to determine general behavioral trends relevant to time-modulated, or pulsed, rf systems. © 1998 American Institute of Physics.

Notes: A solitary kinetic Alfvén wave (SKAW) with a finite ion gyroradius is obtained by using kinetic theory. It is found that the existence of SKAW depends not only on the parallel wave number but also on the perpendicular wave number. In contrast to the results with cold ions, both the super-Alfvénic and the sub-Alfvénic solitons exist in the density compressive region. The amplitude and the parallel propagation velocity of the solitons are found to be enhanced, while the width is narrowed due to the finite ion gyrodius effect. © 1998 American Institute of Physics.

Notes: It is found that traveling wave solutions of the diffusion equation can have propagation times, related to the scale length of the perturbation, which can be considerably less than the characteristic diffusion times. This provides a possible model for the interpretation of recent experiments of fast "hot" and "cold" pulses in magnetically confined plasmas. © 1998 American Institute of Physics.

Notes: The influence of foams on laser shocks was studied with ns laser pulses smoothed with phase zone plates and focused onto layered foam–aluminum targets. Foams of 5–200 mg/cm3 density and 60 μm thickness were used. A strong pressure increase was measured with the foam in comparison to focusing the beam directly onto aluminum due to impedance mismatch at the aluminum–foam interface. Below a particular density, the measured pressure decreased as a result of hydrodynamics effects. Results are compared with computer simulations. © 1998 American Institute of Physics.

Notes: This work is an analysis of an ion turbulence in a tokamak in the case where the thermal flux is fixed and the temperature profile is allowed to fluctuate. The system exhibits some features of self-organized critical systems. In particular, avalanches are observed. Also the frequency spectrum of the thermal flux exhibits a structure similar to the one of a sand pile automaton, including a 1/f behavior. However, the time average temperature profile is found to be supercritical, i.e., the temperature gradient stays above the critical value. Moreover, the heat diffusivity is not the same for a turbulence calculated at fixed flux than at fixed temperature gradient, with the same time averaged temperature. More precisely the diffusivity at fixed temperature is found to be larger in the edge and smaller close to the heat source. © 1998 American Institute of Physics.

Notes: The modulational instability of random phase Langmuir waves in an unmagnetized collisional plasma is investigated. The growth rate of the instability is presented in several interesting limiting cases. The relevance of this investigation to space and laboratory plasmas is pointed out. © 1998 American Institute of Physics.

Notes: An experimental investigation of the effect of negative ions on shock formation in a (collisional) Q machine plasma is described. Shock formation was observed only when the ratio of the negative ion to positive ion density, ε, exceeded about 0.9. © 1998 American Institute of Physics.

Notes: The forced reconnection of magnetic field lines within the framework of electron magnetohydrodynamics (EMHD) has been investigated. A broad class of solutions that describe stationary reconnection have been found. The time evolution of the plasma and of the magnetic field when perturbations are imposed from the boundary of a high conductivity plasma slab are also studied. The initial magnetic field has a null surface. Following this discussion, the so-called Taylor's problem for EMHD in which the perturbations cause a change in the topology of the magnetic field has been solved. The plasma and the magnetic field are seen to evolve with the time scale of the linear tearing mode. Their time evolution is described by exponential dependences. Analytic and numerical simulation results of the nonlinear regime of forced magnetic reconnection in EMHD are also presented. Finally, the above results are compared with a case where the reconnection is mediated by dissipative electron viscosity effects. © 1998 American Institute of Physics.

Notes: The damping of an ion Bernstein wave (IBW) across a resonant layer of the minority species of the plasma is calculated within the framework of quasilinear theory. The model uses the analytical solution of the one-dimensional Fokker–Planck equation for the ion distribution function. A greater reduction of the damping has been found in this case compared with the one obtained with the linear model. This allows the wave to penetrate further towards the plasma core. In addition, a particle flux induced by the sharp spatial gradient of the distribution function across the resonant layer, due to the IBW field, has also been evaluated. This shows that modification of the distribution function generates a flux of particles from the outside which tends to increase the particle density in the vicinity of the resonance itself. © 1998 American Institute of Physics.

Notes: Nonlinear dynamics and self-oscillations in a dc beam-driven collisional discharge are investigated with particle-in-cell simulation and theoretical estimation. Three different modes, anode-glow, temperature-limited, and double-layer modes, are observed in the system. A theory for the critical voltage of mode transition between temperature-limited and anode-glow modes is in good agreement with the simulation results. The mechanism of low frequency self-oscillation in the double layer mode is examined along with period-doubling and chaotic oscillations. © 1998 American Institute of Physics.

Notes: Minority ion cyclotron current drive is studied by solving the Fokker–Planck equation in toroidal geometry keeping the ∂/∂v(parallel)-term in the quasilinear operator, hereby including the important effects of the finite orbit widths of the tail ions and the wave-induced spatial drift and diffusion. It has previously been found that the trapped ion current and the current carried by passing ions detrapped by wave-induced v⊥-diffusion are the two dominating contributions for high levels of coupled power. In this study yet another current-drive mechanism is presented, asymmetric detrapping by inward wave-induced radial drift, which occurs for negative k(parallel) and is strongest for on-axis resonance where it is the totally dominating effect for high powers. © 1998 American Institute of Physics.

Notes: Analytical investigations and numerical simulations of the influence of frozen-in law violation effects on the turbulent equipartition (TEP) of plasma density n∼1/q through the safety factor q in tokamaks are performed. Namely, the changes of the frozen-in field topology are taken into account due to strong turbulence. The found influence leads to flatter than 1/q density and temperature profiles. For a moderate level of turbulence, another reason for flat equipartition profiles was found analytically, if turbulent mixing of passing electrons takes place. This possibility arises due to conservation of the helicity (AB) integral over frozen-in field lines and produces a flat TEP density profile n∼AB of passing electrons (A is the vector potential of the magnetic field B). These influences have been tested in numerical experiments and the results were compared with experimental data in tokamaks. So, the numerical scaling of combined TEP profile of both trapped and passing electrons is n∼1/q0.5–0.6, which is in good agreement with the experiments. © 1998 American Institute of Physics.

Notes: Suppression mechanism of turbulent thermal-energy transport is studied using the statistical method based on an extended magnetohydrodynamic (MHD) approximation. The one-fluid MHD system of equations is supplemented with effects of electric fields coming from the inhomogeneity of charge density. A Markovianized two-scale method is applied to the resulting system, and the turbulent transport rate of thermal energy is examined. In cylindrical geometry, the transport is shown to be suppressed through the combined effects of the radial electric field and the charge nonuniformity arising from its curvature. This finding is discussed in light of the formation of transport barriers observed in tokamak's high-confinement modes and is confirmed to be consistent with observational results. © 1998 American Institute of Physics.

Notes: Momentum transfer via Kirchhoff radiation of electrostatic electron and ion-cyclotron-harmonic waves contributes an enhanced collisionality far in excess of that given by the Fokker-Planck term in the existing neoclassical models. The resultant particle and thermal transport resembles the observed anomalous transport in ohmically heated toroidal plasmas. © 1998 American Institute of Physics.

Notes: It is shown that the coexistence of toroidally nonlocalized ideal-hydromagnetic ballooning instabilities, with a quasidiscrete spectrum, and toroidally localized ballooning instabilities with a broad continuous spectrum, as predicted by Dewar and Glasser [Phys. Fluids 26, 3038 (1983)] can be realized in a Mercier-unstable equilibrium case modeling the Large Helical Device (LHD) [A. Iiyoshi et al., Fusion Technol. 17, 148 (1990)] with a broad pressure profile. The quasidiscrete, interchange branch corresponds to extended modes that can be understood on the basis of a ripple-averaged ballooning equation, whereas the broad-continuum, ballooning branch corresponds to modes localized along a flux tube. The physical origin of the two branches is discussed. © 1998 American Institute of Physics.

Notes: The ability of an inertial confinement fusion target to achieve ignition and burn depends critically upon controlling the growth of hydrodynamic perturbations originating on the outer ablator surface and the inner deuterium–tritium (DT) ice. The MIMOZA-ND code [Sofronov et al., Voprosy Atomnoy Nauki i Tehniki 2, 3 (1990)] was used to model perturbation growth on both sides of carbon foils irradiated by 0.35 μm light at 1015 W/cm2. When an initial perturbation was applied to a laser irradiated surface, the computational instability growth rates agreed well with the existing theoretical estimates. Perturbations applied to the rear side of the target for wavelengths that are large compared to the thickness (d/Λ(very-much-less-than)1) behave similarly to the perturbations at the ablation front. For d/Λ≥1, the shorter the wave length is, the faster the decrease of the growth rate of the amplitudes at the interface (and the mass flows) as compared to the perturbations at the ablation front. This is due to the Richtmyer–Meshkov instability-induced transverse velocity component. The time of Rayleigh–Taylor instability transition to the nonlinear phase depends on the initial amplitude and is well modeled by an infinitely thin shell approximation. The transverse velocity generated by the Richtmyer–Meshkov instability causes the interaction of Λ=10 μm and Λ=2 μm wavelength modes to differ qualitatively when the perturbations are applied to the ablation front or to the rear side of target. © 1998 American Institute of Physics.

Notes: An explicit mathematical formalism is developed to evaluate the growth rate of field-aligned electromagnetic R-mode waves in a relativistic plasma. The methodology is valid for weak wave growth or damping when the resonant relativistic electrons comprise a small portion of the total plasma population. Numerical results are obtained for realistic plasma parameters using three distinct distribution functions for the relativistic electron population. Wave growth rates obtained by numerical integration along the resonant relativistic ellipse are shown to be substantially smaller than calculations performed under the nonrelativistic approximation. The relativistic corrections are primarily due to a reduction in the resonant electron anisotropy. Changes from the standard nonrelativistic treatment are noticeable at relatively small electron thermal energies (a few keV), and they become very significant for thermal energies above 100 keV, especially in low density regions where the plasma frequency is comparable to or lower than the electron gyrofrequency. The results have applications to wave instability in the outer radiation belts of the Earth, the inner Jovian magnetosphere, and other space plasmas where relativistic electrons are present. © 1998 American Institute of Physics.

Notes: Finite Larmor radius magnetohydrodynamics (FLR MHD), being valid when the ion Larmor radius is of the order of the characteristic length scale, predicts a Rayleigh–Taylor instability in an inhomogeneous plasma with unfavorable field line curvature. It is shown that the FLR MHD equations can be reduced to a set of two scalar field equations for the pressure and the electrostatic potential in the flute approximation and the large aspect ratio limit. Using a Galerkin approximation with a few dominating modes, the simple model reproduces previous numerical simulations based on the full FLR MHD equations. © 1998 American Institute of Physics.

Notes: The effect of subtle changes in initial conditions on the evolution of global quantities in two-dimensional magnetohydrodynamic (MHD) turbulence is studied. It is found that a change in the initial phases of complex Fourier modes of the Elsässer variables, while keeping the initial values of total energy, cross helicity, and Alfvén ratio unchanged, has a significant effect on the evolution of cross helicity. On the contrary, the total energy and Alfvén ratio are insensitive to the initial phases. The simulations are based on direct numerical simulation using the pseudospectral method. © 1998 American Institute of Physics.

Notes: Tearing-type modes are observed in most high confinement operation regimes in the Tokamak Fusion Test Reactor (TFTR) [Nucl. Fusion 35, 1429 (1995)]. Three different methods are used to measure the magnetic island widths: external magnetic coils, internal temperature fluctuation from electron cyclotron emission (ECE) diagnostics and an experiment where the plasma major radius is rapidly shifted ("Jog" experiments). A good agreement between the three methods is observed. Numerical and analytic calculations of Δ′ (the tearing instability index) are compared with an experimental measurement of Δ′ using the tearing mode eigenfunction mapped from the jog data. The obtained negative Δ′ indicates that the observed tearing modes cannot be explained by the classical current-gradient-driven tearing theory. © 1998 American Institute of Physics.

Notes: Brillouin scattering from a preformed, inhomogeneous, expanding plasma has been investigated. Backscattered light near the incident laser wavelength (λ=1054 nm) from CH planar targets has been spectrally and temporally resolved. By varying the time delay of the interaction beam, the scattering was studied for different plasma conditions. The backscattered light is predominantly blue-shifted and appears before the peak of the laser pulse. The experimental time-integrated reflectivity of backscattered light is in the range of 1%–10% and decreases with the plasma density. The time-resolved spectra and total reflectivity were calculated using a theory of convective stimulated Brillouin scattering (SBS) in a flowing inhomogeneous plasma combined with a statistical hot spot model for the interaction beam. The plasma parameters for these calculations were provided by simulations using a two-dimensional hydrodynamic code. The calculated SBS spectra are similar to the experimental observations. The time-integrated reflectivities agree well with the experimental results for the higher peak density interactions, but are below the observations by orders of magnitude for the lowest peak density cases. © 1998 American Institute of Physics.

Notes: A fully electromagnetic particle in cell-Monte Carlo (PIC-MCC) code is considered for the ballistic transport of intense ion beams in a reaction chamber field with Flibe gas surrounding a pellet with a thermonuclear fuel in it. A specific emphasis is given to a self-consistent treatment of beam boundary conditions. Spurious electromagnetic waves are evacuated out of the grid, and a modified Maxwell system corrects for Gauss theorem error. A dynamical grid with self-adaptating field follows beam convergence. Final ion propagation in the Hylife II [R. Moir, Fusion Technol. 29, 306 (1991)] scheme and also in the space charge compensated one is investigated at length. For the first, a partial beam neutralization is identified only through electron background. The second displays an acceptable focalization at pellet, the background electron temperature has a significant influence on beam minimum radius. Transverse emittance is given specific attention.© 1998 American Institute of Physics.

Notes: The Kelvin–Helmholtz (K-H) instability of two fluids of a plasma, streaming in opposite directions with the same velocity and in the presence of an external magnetic field, is investigated. The external magnetic field in both fluids are in different directions. The usual magnetohydrodynamic (MHD) equations with anisotropic pressures are considered. The generalized pressure relation is used and two equations of state for two pressures are taken up in the problem. The equations are linearized and initially two different flow velocities are taken for the system. The problem is solved and a dispersion relation is obtained. It is found that the instability condition for the static configuration depends on the polytropic index of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low (CGL) systems. For the nonstatic streaming configuration it is also found that growth rate of K-H instability depends on various polytropic indices and magnetic field. © 1998 American Institute of Physics.

Notes: An experimental study of optical probing of a dense z-pinch plasma using the MAGPIE (mega-ampere generator for plasma implosion experiments) generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)] is reported. The generator was operated with a peak current of 1.1 MA rising in 150 ns (10%–90%). The loads were 33 μm diam carbon fibers. Faraday rotation was used to investigate the distribution of the current flowing in the plasma. A measurable Faraday rotation angle was observed only in a time window from 50 to 60 ns after the current start, due to the fact that this effect depends on a combination of the magnetic-field strength and electron number density. A new type of self-referencing cyclic radial shear interferometer was used to evaluate the plasma density profiles which are necessary for the reconstruction of the current distribution. It was calculated that ∼110 kA was flowing in the plasma at 52 ns after the current start. Shadowgraphy was used to study the dynamics of the plasma and to investigate the formation of instabilities. Plasma instabilities were observed at very early times (∼5 ns). These instabilities appeared to be not entirely axi-symmetric implying the existence of m=1 and maybe higher modes as well as m=0. The perturbations increased with time and evolved into density islands (isolated plasma fragments) distributed along the axis at late times (∼70 ns). © 1998 American Institute of Physics.

Notes: A set of three coupled ordinary differential equations that give the evolution of the density, the radial electric field, and poloidal plasma rotation are derived from the continuity equation and momentum balance. They include the effect of those processes considered to be of importance for the L- (low) to H- (high) mode transition: neutral friction, neoclassical viscosity, the radial pressure gradient, orbit losses, a radial current through a probe, anomalous stresses, and Stringer spin up. The equations are valid for arbitrary toroidally symmetric geometry and include effects of non-uniformity (of for instance the neutral friction) in the magnetic surface. As an example, non-uniform neutral friction in an elongated geometry is discussed. © 1998 American Institute of Physics.

Notes: Two-dimensional ideal magnetohydrodynamic (MHD) simulations are presented that demonstrate several novel phenomena in MHD shock formation. The stationary symmetrical flow of a uniform, planar, field-aligned, low-β and superfast magnetized plasma around a perfectly conducting cylinder is calculated. The velocity of the incoming flow is chosen such that the formation of fast switch-on shocks is possible. Using a time marching procedure, a stationary bow shock is obtained, composed of two consecutive interacting shock fronts. The leading shock front has a dimpled shape and is composed of fast, intermediate and hydrodynamic shock parts. A second shock front follows the leading front. Additional intermediate shocks and tangential discontinuities are present in the downstream part of the flow. The intermediate shocks are of the 1–3, 1–4, 2–4 and 1=2–3=4 types. This is a confirmation in two dimensions of recent results on the admissibility of these types of shocks. Recently it has also been shown that the 1=2–3=4 shock, embedded in a double compound wave, is present in the analytical solution of some planar one-dimensional MHD Riemann problems. This MHD flow with interacting shocks may have applications for some observed features of fast solar Coronal Mass Ejections and other phenomena in low-β space plasmas. © 1998 American Institute of Physics.

Notes: A theory of plasma-filled traveling-wave tubes (TWTs) is developed in which the effect of magnetosonic waves excited in plasma by the operating wave is taken into account. These waves are excited by the ponderomotive force caused by the radial inhomogeneity of the axial component of the electric field of the operating wave. In the simplest case considered in the paper, this effect leads to an additional reactive nonlinearity in the wave envelope equation. This leads to a shrinkage of the region of stable oscillations in TWTs with the feedback causing the self-excitation; at the same time, the region of stochastic oscillations becomes larger. The radiation spectrum of stochastic oscillations in plasma-filled TWTs in which magnetosonic waves are excited is much wider and more continuous than the spectrum of stochastic oscillations in vacuum TWTs with the same feedback. © 1998 American Institute of Physics.

Notes: The structure and spectrum of magnetosonic Alfvén eigenmodes in a spherical torus in the presence of a magnetic field well are studied. Analytical solution for eigenmodes localized in the well is obtained and compared with the numerical one. The possibility of using the eigenmode spectrum measurements for reconstructing the magnetic field well, and, thus, the central magnetic safety factor profile, is discussed. © 1998 American Institute of Physics.

Notes: Experimental observation of the cross-excitation instability in a relativistic backward wave oscillator is reported. The transition between single frequency operation and the cross-excitation regime is measured. The initial mode excited in the cross-excitation regime has a relatively low efficiency, while the second mode has considerably higher efficiency and a slightly higher frequency. The two modes are observed to be beating for a considerable fraction of the radiated microwave pulse. These results are consistent with earlier theoretical predictions for the onset and voltage scaling for this instability. © 1998 American Institute of Physics.

Notes: Mechanisms for the confinement and the internal structure of an electrostatically coupled dust cloud formed in a dc glow discharge have been investigated from a comparative viewpoint between experimental observations and a simple model. Two kinds of dust clouds with different internal structures are clearly observed, depending on the dispersion of the size distribution of dust particles. The dust cloud can be trapped only in the plasma–sheath boundary area, corresponding to the potential minimum region determined by gravitational and electrostatic forces in the cathode sheath. No dust particles were found deep inside of the sheath, which is consistent with the analysis because the dust particles may be charged positively due to an extreme reduction of the electron density. The internal structure of the electrostatically coupled dust cloud was found to be arranged so that the total potential energy, including the repulsive Coulomb interaction among negative dust particles, may become minimal. © 1998 American Institute of Physics.

Notes: The influence of strong correlations on low frequency collective modes in a dusty plasma is investigated. The dust dynamics is modeled by the generalized hydrodynamics description. For the well known dust acoustic mode, strong correlations lead to new dispersive corrections, an overall reduction of the frequency and phase velocity and the existence of parameter regions where ∂ω/∂k〈0. A novel result is the possibility of sustaining a low frequency transverse mode—a dust shear mode—in which the correlation energy acts as an effective bulk modulus. The influence of ion streaming and collisional interaction with a background of neutrals on the modes are also studied and it is shown that the longitudinal modes may be driven unstable by ion streaming. © 1998 American Institute of Physics.

Notes: In this paper we propose a new method to calculate the plasma dispersion relation for a wide variety of distribution functions with a complicated resonance mechanism. An approximation with a one-over-polynomial function enables us to apply the residue theorem for integration, and gives an analytical form of the dispersion equation. The solution is highly accurate with typical error less than 10−4 when applied to the ordinary plasma dispersion function (Z function). Application of this method is not limited to the dispersion functions that can be expressed by the Z function; it can be applied to much wider class of problems with arbitrary velocity distributions. One example is the general solution to the dispersion equation for a weakly relativistic magnetized plasma. © 1998 American Institute of Physics.

Notes: A model is presented which describes the nonlinear interaction of dispersive shear Alfvén wave (SAW) field line resonances (FLRs) and ion acoustic waves (IAWs), with applications to the Earth's magnetosphere. Two limits are considered: In low-β plasma (β〈me/mi), dispersion is dominated by electron inertia (EI), while for higher β it is dominated by the electron thermal effect. In each case, the ponderomotive force steepens the SAW in the radial direction, taken as earthward in the equatorial plane. Following the time of nonlinear steepening, the dynamics strongly depends on dispersion. In the EI case, standing SAWs excited in FLRs exhibit a parametric decay instability (PDI) into secondary SAWs and IAWs. Nonlinearity and dispersion broaden the FLR in the radial direction, leading to rapid density and parallel electric field fluctuations and scale lengths comparable to the EI length. In warm plasmas, SAWs are stable to the PDI, and in this case the FLR emits short perpendicular scale SAW-IAW solitons in the anti-earthward direction. Observational consequences of both scenarios are discussed. © 1998 American Institute of Physics.

Notes: The stability analysis of a high-β toroidal tokamak plasma is carried out in the presence of toroidal flow, finite plasma resistivity, and a surrounding shell of finite electrical resistivity. The beta limits for the n=1 mode are set by the resistive-wall-tearing mode (RWTM), the ideal-wall-tearing mode (IWTM), and the ideal-plasma-resistive-wall mode (IPRWM). Slow plasma rotation suppresses the RWTM while the IPRWM is not directly affected by slow plasma flow. For small plasma resistivity, the IPRWM is stabilized by fast flow only. For large plasma resistivity, the IPRWM only exists in a plasma rotating faster than the typical tearing mode growth rate, and its instability threshold is a complicated function of the wall position and rotation frequency. Very fast rotation can destabilize the ideal kink through centrifugal effects. Furthermore, for b/a (wall radius/plasma radius) below a critical value, a stationary plasma is stable to the n=1 ideal kink and tearing mode for large values of β. © 1998 American Institute of Physics.

Notes: The ideas and the conceptual steps leading from the ergodic hypothesis for equilibrium statistical mechanics to the chaotic hypothesis for equilibrium and nonequilibrium statistical mechanics are illustrated. The fluctuation theorem linear law and universal slope prediction for reversible systems is briefly derived. Applications to fluids are briefly alluded to. © 1998 American Institute of Physics.

Notes: Anomalous transport is investigated near threshold in the standard map. Very long time flights, and a large anomaly in the transport, are shown to be associated with a new form of multi-island structures causing orbit sticking. The phase space structure of these traps, and the exponents of the characteristic long time tails associated with them are determined. In general these structures are very complex, but some cases, consisting of layers of islands, allow simple modeling. © 1998 American Institute of Physics.

Notes: We consider the problem of nonlinear noise reduction within the framework of Bayesian Theory. This enables us to place appropriate weights on the measurement and dynamic errors and thereby avoid over cleaning the data. Using a Metropolis–Hastings sampler, we are able to achieve robust noise reduction without the introduction of ad hoc parameters but at the expense of higher computational complexity. Such an algorithm should also allow us to explore the potential and limitations of other noise reduction methods. © 1998 American Institute of Physics.

Notes: We describe a method for introducing variations into predefined motion sequences using a chaotic symbol-sequence reordering technique. A progression of symbols representing the body positions in a dance piece, martial arts form, or other motion sequence is mapped onto a chaotic trajectory, establishing a symbolic dynamics that links the movement sequence and the attractor structure. A variation on the original piece is created by generating a trajectory with slightly different initial conditions, inverting the mapping, and using special corpus-based graph-theoretic interpolation schemes to smooth any abrupt transitions. Sensitive dependence guarantees that the variation is different from the original; the attractor structure and the symbolic dynamics guarantee that the two resemble one another in both aesthetic and mathematical senses. © 1998 American Institute of Physics.

Notes: Cryptosystems for binary information are based on two primitives: an indexed family of permutations of binary words and a generator of pseudorandom sequences of indices. A very efficient implementation of the primitives is constructed using the phenomenon of synchronization in cellular automata. © 1998 American Institute of Physics.

Notes: We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from amplitudes to physical space. At any order, the relation provides explicit expressions for all the nonvanishing coefficients of the amplitude equation together with straightforward linear equations for the coefficients of the transformation. The recurrence relation therefore provides all the machinery needed to solve a given physical problem in physical terms through an amplitude equation. The new result applies to any local bifurcation of a flow or map for which all the critical eigenvalues are semisimple (i.e., have Riesz index unity). The method is an efficient and rigorous alternative to more intuitive approaches in terms of multiple time scales. We illustrate the use of the method by deriving amplitude equations and associated transformations for the most common simple bifurcations in flows and iterated maps. The results are expressed in tables in a form that can be immediately applied to specific problems. © 1998 American Institute of Physics.

Notes: A recurrence plot is a visualization tool for analyzing experimental data. These plots often reveal correlations in the data that are not easily detected in the original time series. Existing recurrence plot analysis techniques, which are primarily application oriented and completely quantitative, require that the time-series data first be embedded in a high-dimensional space, where the embedding dimension dE is dictated by the dimension d of the data set, with dE≥2d+1. One such set of recurrence plot analysis tools, recurrence quantification analysis, is particularly useful in finding locations in the data where the underlying dynamics change. We have found that for certain low-dimensional systems the same results can be obtained with no embedding. © 1998 American Institute of Physics.

Notes: We show that the conventional stochastic resonance (SR) effect for aperiodic signals in a model neuron can be enhanced by modulating the intensity of the input noise (which could be introduced artificially in bioengineering applications) with either the input signal or the unit's output rate signal. We analyze SR enhancement theoretically and numerically. We discuss how this work provides the theoretical foundation for the development of an optimal noise-based technique for enhancing sensory function. © 1998 American Institute of Physics.

Notes: The constructive role of random fluctuations is studied in the context of transport in stochastic ratchets. We discuss the interplay of independent white (thermal) and discrete (external) noises and their generation of transport in anisotropic potentials. The constructive cooperation of such fluctuations is most apparent in the asymptotic limit of fast discrete-valued noise, a limit which presents some interesting mathematical features. We describe the asymptotic analysis of the current in the limit of fast external noise, pointing out the strong qualitative dependence of the current on the interplay of the independent noise sources and its surprising sensitivity to the regularity of the underlying anisotropic ratchet potential. © 1998 American Institute of Physics.

Notes: The subject of this paper is the construction of the exponential asymptotic expansions of the unstable and stable manifolds of the area-preserving Hénon map. The approach that is taken enables one to capture the exponentially small effects that result from what is known as the Stokes phenomenon in the analytic theory of equations with irregular singular points. The exponential asymptotic expansions were then used to obtain explicit functional approximations for the stable and unstable manifolds. These approximations are compared with numerical simulations and the agreement is excellent. Several of the main results of the paper have been previously announced in A. Tovbis, M. Tsuchiya, and C. Jaffé ["Chaos-integrability transition in nonlinear dynamical systems: exponential asymptotic approach," Differential Equations and Applications to Biology and to Industry, edited by M. Martelli, K. Cooke, E. Cumberbatch, B. Tang, and H. Thieme (World Scientific, Singapore, 1996), pp. 495–507, and A. Tovbis, M. Tsuchiya, and C. Jaffé, "Exponential asymptotic expansions and approximations of the unstable and stable manifolds of the Hénon map," preprint, 1994]. © 1998 American Institute of Physics.

Notes: We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky reaction. An arbitrary binary message is encoded by forcing the chaotic oscillations to follow a specified trajectory. The information manipulating control requires only small perturbations to vary the binary message. In this paper we extend our recent theoretical work [Bollt and Dolnik, Phys. Rev. E 64, 1196 (1990)] by introducing a new and simplified encoding technique which can be utilized in the presence of experimental noise. We numerically and theoretically study several practical aspects of controlling symbol dynamics including: modeling noisy time-series, learning underlying symbol dynamics, and evaluation of derivatives for control by observing system responses to an intelligent and deliberate sequence of input parameter variations. All of the modeling techniques incorporated here are ultimately designed to learn and control symbol dynamics of experimental data known only as an observed time-series; the simulation assumes no global model. We find that noise affects reliability of encoding information and may cause coding errors. But, if the level of noise is confined to relatively small values, which are achievable in experiments, the control mechanism is robust to the noise. Thus we can still produce a desired symbolic code. However, scarce errors in encoding may occur due to rare but large fluctuations. These errors may be corrected during the decoding process by a variation of the filtering technique suggested by Rosa et al. [Phys. Rev. Lett. 78, 1247 (1997)]. © 1998 American Institute of Physics.

Notes: The probabilistic approach to dynamical systems giving rise to irreversible behavior at the macroscopic, mesoscopic, and microscopic levels of description is outlined. Signatures of the complexity of the underlying dynamics on the spectral properties of the Liouville, Frobenius–Perron, and Fokker–Planck operators are identified. Entropy and entropy production-like quantities are introduced and the connection between their properties in nonequilibrium steady states and the characteristics of the dynamics in phase space are explored. © 1998 American Institute of Physics.

Notes: The multifractal link between chaotic time-reversible mechanics and thermodynamic irreversibility is illustrated for three simple chaotic model systems: the Baker Map, the Galton Board, and many-body color conductivity. By scaling time, or the momenta, or the driving forces, it can be shown that the dissipative nature of the three thermostated model systems has analogs in conservative Hamiltonian and Lagrangian mechanics. Links between the microscopic nonequilibrium Lyapunov spectra and macroscopic thermodynamic dissipation are also pointed out. © 1998 American Institute of Physics.

Notes: We consider a dynamical system with state space M, a smooth, compact subset of some Rn, and evolution given by Tt, xt=Ttx, x∈M; Tt is invertible and the time t may be discrete, t∈Z, Tt=Tt, or continuous, t∈R. Here we show that starting with a continuous positive initial probability density ρ(x,0)〉0, with respect to dx, the smooth volume measure induced on M by Lebesgue measure on Rn, the expectation value of logρ(x,t), with respect to any stationary (i.e., time invariant) measure ν(dx), is linear in t, ν(logρ(x,t))=ν(logρ(x,0))+Kt. K depends only on ν and vanishes when ν is absolutely continuous with respect to dx.© 1998 American Institute of Physics.

Notes: An approach for the secure transmission of encrypted messages using chaos and noise is presented in this paper. The method is based on the synchronization of certain types of chaotic oscillators in response to a common noise input. This allows two distant oscillators to generate identical output which can be used as a key for encryption and decryption of a message signal. The noiselike synchronizing input—which contains no message information—is communicated to identical oscillators in the transmitter and the receiver over a public channel. The encrypted message is also sent over a public channel, while the key is never transmitted at all. The chaotic nature of the oscillators which generate the key and the randomness of the signal driving the process combine to make the recovery of the key by an eavesdropper extremely difficult. We evaluate system performance with respect to security and robustness and show that a robust and secure system can be obtained. © 1998 American Institute of Physics.

Notes: The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state, are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas. © 1998 American Institute of Physics.

Notes: This paper describes a laboratory study on the evolution of a point turbulent plume placed at the free surface of a homogeneous fluid layer in the presence of background rotation. It is shown that the plume initially evolves as if there is no rotation. However, the rotational effects become important after the plume descends a vertical distance hc1(approximate)3.3(B/Ω3)1/4 for a normalized time Ωtc1(approximate)2.4, whence the vertical descent rate of the plume is reduced while maintaining approximately the same lateral growth rate. Here Ω is the rate of background rotation and B is the specific buoyancy flux of the plume. The rotational effects inhibit the lateral growth of the plume at a time Ωtc2(approximate)5.5, when the maximum plume width is bc(approximate)1.4(B/Ω3)1/4. Thereafter, the vertical descent continues and the plume evolves into a cylindrical shape while developing a cyclonic circulation in and around it, except near the plume front. Upon reaching the bottom surface after traveling a fluid depth of H, the plume deflects, propagates horizontally, and becomes unstable breaking up into anticyclonic eddies. Studies carried out for the case of H〈hc1 show that this instability is initiated at a horizontal length scale proportional to the Rossby deformation radius of the deflected flow, and hence it is of baroclinic type. These eddies appear to align vertically with the cyclonic eddies formed by the barotropic instability of the surface rim current, thus producing heton-like structures. The influence of the diameter d0 of the plume on the flow evolution is also studied, and it is shown that plumes with aspect ratio h/d0〈12 (where h is the vertical extent) can be approximated as point plumes. Scaling arguments are advanced to explain the results. Some geophysical applications of the study are also discussed. © 1998 American Institute of Physics.

Notes: We consider two-dimensional waves in a rectangular container which is periodically excited along its length in the horizontal direction. In general a standing wave of odd mode number whose frequency is close to the forcing frequency is excited. However, we show in this paper that the neighboring even mode, though not directly excited, may be excited through an energy transfer from the odd mode. As a result, the wave response becomes superposition of two standing waves which are not in general in phase with each other. Consequently the mixed-mode wave motion is not standing waves but traveling waves. We employ a perturbation method to derive amplitude equations governing the dynamics of these two modes. Studies of the steady-state solutions and their stability lead to bifurcation diagrams showing the sequences of the events leading to the instability and the parameters for which the standing waves become unstable. © 1998 American Institute of Physics.

Notes: We consider the motion of a spherical annulus of fluid driven by the slightly differential rotation of the confining spherical shells. The novelty of our analysis is the imposition of a strong axisymmetric potential magnetic field on a conducting annulus bounded by insulators. The strength of the field is measured by its ability to dominate the dynamics of the fluid shell, being much larger than the viscous and Coriolis forces. The fluid flow is structured such as to minimize the effect of the strong field and the associated induction currents. The thrust of the analysis is the identification of regions of the fluid shell in which the azimuthal flow and generated field are relatively uniform. These regions are bounded by shear layers in which the azimuthal flow and field vary rapidly. Thickness of the shears is about a square root of a Hartmann layer thickness. These Hartmann boundary layers control main streams in the magnetohydrodynamic flow. An imposed axial magnetic field produces two rigid-body rotating regions that have different rotation rates outside and inside the axial cylinder tangent to the inner sphere. The azimuthal magnetic field is proportional to the cylindrical radius and is expelled from the outside of the tangent cylinder. For an imposed dipole magnet, similar regions with rigid-body rotation are divided by a shear that has a shape of a lobe touching the outer equator. Very weak meridional fluid flux is inversely proportional to a cube of the imposed magnetic field for these degenerated cases. In a quadrupole magnetic field, two lobe-like regions are symmetric with respect to the shell's equator, touch the outer sphere, and rotate with the inner sphere. Outside these regions, differential rotation is valuable and a weak meridional fluid flux is inversely proportional to a square of the imposed magnetic field as in the general case. © 1998 American Institute of Physics.

Notes: The equation relating the average rate of change of disturbance kinetic energy to the rates of work done by the surface tension, the shear stress, the Reynolds stress, and the rate of mechanical energy dissipation through viscosity in a falling liquid film flow down an oscillating vertical plate is obtained. Each term in the equation is evaluated in various regions of parameter space to elucidate the physical mechanism of stabilizing an inherently unstable vertical film flow by use of plate oscillations [Lin, Chen, and Woods, Phys. Fluids 8, 3247 (1996); Lin and Chen, Phys. Fluids 9, 3926 (1997)]. © 1998 American Institute of Physics.

Notes: Liquid capsules with an elastic membrane surface in simple shear flow are considered beyond the regime of small deformations. A simple model is introduced to give a mathematical description of an elastic membrane in viscous flow. The question of whether there is a steady state of a system of a single membrane in external shear flow is studied. It is found by analytical considerations that the possible steady-state flows are restricted by symmetry. The evolution of the membrane in time is found by numerical calculations. For a single spherically symmetric membrane, I find by numerical simulations, a steady-state shape and its dependence on the shear strength. For nonspherically symmetric membranes we see that there is no steady-state shape in general, but by numerical simulations I find that the shape changes can become periodic. This leads to a new alternative explanation of previous experimental results. The stress tensor of the membranes and the effective viscosity of a dilute system of elastic membranes immersed in a liquid is calculated. I find an agreement with former analytical calculations for small shear, and obtain shear thinning behavior when the shear rate is increased. © 1998 American Institute of Physics.

Notes: The impact of the nonlinearity in the equation of state associated with the change in the thermal expansion coefficient with temperature on the structure of fingers growing from an interface between two mixed layers is investigated using a numerical model. It is shown that the nonlinearity acts to enhance the buoyancy force acting on the descending fingers with respect to that acting on the ascending fingers, resulting in narrower and faster-growing descending fingers than ascending fingers. The results are discussed with emphasis on the vertical variability of properties along the fingers. © 1998 American Institute of Physics.

Notes: Flow patterns of two-dimensional natural convection in a vertical air-filled tall cavity with differentially heated sidewalls are investigated. Numerical simulations based on a finite difference method are carried out for a wide range of Rayleigh numbers and aspect ratios from the onset of the steady multicellular flow, through the reverse transition to the unicellular pattern, to the unsteady multicellular flow. For aspect ratios (height/width) from 10 to 24, the various cellular structures characterized by the number of secondary cells are clarified from the simulations by means of gradually increasing Rayleigh number to 106. Unsteady multicellular solutions are found in some region of Rayleigh numbers less than those at which the reverse transition has occurred. © 1998 American Institute of Physics.

Notes: A slot with applied temperature stratification is considered when mean gravity is directed along its length and weak quasistatic jitter is applied in the spanwise direction, but when there is no component of gravity in the vertical. The behavior of the slot is governed by a number of factors: The sense of the mean gravity with respect to the applied stratification, the spanwise and lengthwise Rayleigh numbers, the Prandtl and Biot numbers, and the spanwise–lengthwise aspect ratio of the slot. A perturbation expansion of the governing equations is performed for weak spanwise jitter. At the first order of perturbation there is a circulation around the slot, producing an advected temperature field with spanwise gradients. At second order there are inflows or outflows in both the spanwise and lengthwise directions, along with a vertical redistribution of fluid. There is also a temperature field with lengthwise gradients, which typically competes with the applied temperature gradient. Equations are derived governing the vertical structure of all these fields and are solved in terms of a set of special basis functions. A parametric study is performed for the solutions. When lengthwise buoyancy forces are absent (the lengthwise Rayleigh number is zero), it is comparatively easy to deduce the required fields. However, finite lengthwise Rayleigh numbers couple the momentum and thermal equations thereby affecting the structure of the fields. Interesting behavior is predicted for small Biot numbers, when convected heat is effectively trapped in the slot: Infinitessimal flows can produce finite advected temperatures. The limits of small Biot number and small lengthwise Rayleigh number are found to be noninterchangeable. At large lengthwise Rayleigh number, boundary layers occur for stable applied stratification and layered cellular structures occur for unstable stratification. For the stable case at moderately small Biot number, the temperature jump across the boundary layer is small compared with the depth independent temperature in the bulk. Then by exploiting the boundary layer nature of the solutions, it becomes simple to predict the bulk fluid temperatures, interfacial heat fluxes and the circulations associated with the buoyant flows. Turning to the unstably stratified case, it is demonstrated that runaways can occur at first order in the spanwise jitter, and these correspond to resonant excitation of three-dimensional, stationary, long wave Rayleigh–Bénard modes. It is demonstrated how the Biot number and the spanwise–lengthwise aspect ratio of the slot influence the lengthwise Rayleigh number at which these resonances occur. There is in addition a set of two-dimensional Rayleigh–Bénard modes, which can potentially become excited at second order. When the Biot number and the spanwise–lengthwise aspect ratio are not too large, the Rayleigh numbers corresponding to the two sets of modes are nearly coincident. The second-order system will then be strongly forced near resonance, causing it to have a disproportionately large response. © 1998 American Institute of Physics.

Notes: We describe a new dynamic light scattering technique for measuring diffusion in sheared suspensions. It involves a scattering geometry with two crossing laser beams. A detailed analysis of the correlation function of scattered light is given. The viability of our method is demonstrated in an experiment where the effect of Taylor diffusion on the scattered light correlation function is measured. © 1998 American Institute of Physics.

Notes: Magnetic levitation was used to stabilize cylindrical columns of a paramagnetic liquid in air between two solid supports. The maximum achievable length to diameter ratio Rmax was ∼(3.10±0.07), very close to the Rayleigh–Plateau limit of π. For smaller R, the stability of the column was measured as a function of the Bond number, which could be continuously varied by adjusting the strength of the magnetic field. © 1998 American Institute of Physics.

Notes: A method has been developed to drive a cylindrical liquid jet unstable for deformations with axial wavelengths shorter than the circumference of the jet and azimuthal mode numbers greater than 0. The benefit of this method is that a cylindrical liquid jet can be broken into a spray with an average diameter smaller than the diameter of the initial jet. The higher-order instabilities were created by establishing initial conditions for the jet in space and time at the nozzle. An electromechanical transducer creates the applied temporal initial condition which is a sinusoidally varying velocity perturbation added to the steady velocity of the jet. The amplitude of the velocity perturbation can be as large as the jet's steady velocity and the energy in the applied velocity perturbation drives the instability. The spatial perturbation is created by placing perturbations in the circumference of the nozzle. As the velocity perturbation travels on the jet, its leading edge steepens and the trailing edge broadens in a manner analogous to the steepening of a pressure pulse in a compressible gas. If the driven velocity perturbation is sufficiently large, a shock or jump forms on the leading edge of the velocity pulse and the jet may break up into higher-order modes. A theoretical analysis of the breakup process, based on an adaptation of compressible fluid shock theory, is used to derive a fundamental lower bound on the spray's Sauter mean diameter as a function of the velocity perturbation amplitude. Techniques for approaching the theoretical minimum spray diameter by using the higher-order modes to atomize liquid jets are discussed. © 1998 American Institute of Physics.

Notes: A nominally plane turbulent jet is synthesized by the interactions of a train of counter-rotating vortex pairs that are formed at the edge of an orifice by the time-periodic motion of a flexible diaphragm in a sealed cavity. Even though the jet is formed without net mass injection, the hydrodynamic impulse of the ejected fluid and thus the momentum of the ensuing jet are nonzero. Successive vortex pairs are not subjected to pairing or other subharmonic interactions. Each vortex of the pair develops a spanwise instability and ultimately undergoes transition to turbulence, slows down, loses its coherence and becomes indistinguishable from the mean jet flow. The trajectories of vortex pairs at a given formation frequency scale with the length of the ejected fluid slug regardless of the magnitude of the formation impulse and, near the jet exit plane, their celerity decreases monotonically with streamwise distance while the local mean velocity of the ensuing jet increases. In the far field, the synthetic jet is similar to conventional 2D jets in that cross-stream distributions of the time-averaged velocity and the corresponding rms fluctuations appear to collapse when plotted in the usual similarity coordinates. However, compared to conventional 2D jets, the streamwise decrease of the mean centerline velocity of the synthetic jet is somewhat higher (∼x−0.58), and the streamwise increase of its width and volume flow rate is lower (∼x0.88 and ∼x0.33, respectively). This departure from conventional self-similarity is consistent with the streamwise decrease in the jet's momentum flux as a result of an adverse streamwise pressure gradient near its orifice. © 1998 American Institute of Physics.

Notes: Two-dimensional nonlinear equilibrium solutions for the swept Hiemenz flow attachment line boundary layer are directly computed by solving the full Navier-Stokes equations as a nonlinear eigenvalue problem. The equations are discretized using the two-point fourth order compact scheme and the resulting nonlinear homogeneous equations are solved using the Newton-Raphson iteration technique. It is found that for Reynolds numbers larger than the linear critical Reynolds number of 583, the nonlinear neutral surfaces form open curves. The results showed that the subcritical instability exists near the upper branch neutral curve and supercritical equilibrium solutions exist near the lower branch. These conclusions are in agreement with the weakly nonlinear theory. However, at higher amplitudes away from the linear neutral points the nonlinear neutral surfaces show subcritical instability at lower and higher wave number regions. At Reynolds numbers lower than the critical value, the nonlinear neutral surfaces form closed loops. By reducing the Reynolds number, we found that the nonlinear critical point occurs at a Reynolds number of 511.3, below which all the two-dimensional disturbances will decay. The secondary instability of these equilibrium solutions is investigated using the Floquet theory. The results showed that these two-dimensional finite amplitude neutral solutions are unstable to three-dimensional disturbances. © 1998 American Institute of Physics.

Notes: We report experimental measurements of Lagrangian accelerations in a turbulent water flow between counter-rotating disks for Taylor–Reynolds numbers 900〈Rλ〈2000. Particle tracks were recorded by imaging tracer particles onto a position sensitive photodiode, and Lagrangian information was obtained from fits to the position versus time data. Several challenges associated with extracting Lagrangian statistical quantities from particle tracks are addressed. The acceleration variance is obtained as a function of Reynolds number and shows good agreement with Kolmogorov (1941) scaling. The Kolmogorov constant for the acceleration variance is found to be a0=7±3. © 1998 American Institute of Physics.

Notes: Results from large eddy simulations (LES) and direct numerical simulations (DNS) of a two-dimensional, spatially developing, compressible planar free jet undergoing an idealized, exothermic, chemical reaction of the type F+rOx→(1+r)P are presented in order to assess several subgrid-scale (SGS) combustion models. Both a priori and a posteriori assessments are conducted. The SGS turbulence model used is the dynamic Smagorinsky model (DSM). Two classes of SGS combustion models are employed in this study. These include the conserved scalar approach and the direct closure approach. Specifically, the SGS combustion models involve several forms of direct filtered reaction rate closures, including a scale similarity filtered reaction rate model (SSFRRM), and a mixing controlled strained laminar flamelet model (SLFM) in the form of thermochemical state relationships, obtained from the DNS, and two assumed forms for the subgrid mixture fraction filtered density function (FDF). In general, LES results are in reasonable agreement with DNS results and highlight the performance of the various SGS combustion models. In particular, in the context of the present study, it is found that: (1) the SLFM cases overpredict product formation due to their inability to capture finite-rate chemistry effects; (2) due to the relatively low values of the SGS mixture fraction variance in the flow under study, the SLFM results are not sensitive to the form of the assumed FDF; and (3) in comparison to the other models investigated, the SSFRRM combustion model provides the best agreement with the DNS for product formation. © 1998 American Institute of Physics.

Notes: The evolution of the invariants (R and Q) of the velocity gradient tensor in homogeneous isotropic turbulence is investigated using data from direct numerical simulation (DNS). The concepts of conditional average time rate of change of the invariants and conditional mean trajectories (CMT) in invariant phase space are introduced to study the dynamics of this flow. The resulting dynamical system in the (R,Q) phase space is a clockwise spiral with a stable focus at the origin, illustrating that in the mean, the cyclic sequence of topological evolution following a fluid particle is unstable-node/saddle/saddle (UN/S/S)→stable-node/saddle/saddle (SN/S/S)→stable-focus/stretching (SF/S)→unstable-focus/contracting (UF/C). The mean rates of change of R and Q, i.e., R(overdot), Q(overdot), are found to be negligible near the right branch of the null discriminant (D=0) curve, indicating that this curve is an attractor in the (R,Q) space. The effects of both the diffusion term and the anisotropic part of the pressure Hessian term on the dynamics of the invariants have also been analyzed using the conditional averages. Both contributions are found to be important in the dynamics of the velocity gradient invariants. Based on these results the extent of the validity of the model equations governing the evolution of R and Q proposed by Cantwell [Phys. Fluids A 4, 782 (1992)] and Dopazo et al. ["Velocity gradients in turbulent flows. Stochastic models," Ninth Symposium on "Turbulent Shear Flows," Kyoto, Japan, 1993, pp. 26-2-1–26-2-5] are discussed. © 1998 American Institute of Physics.

Notes: This article considers the topology of the vortex regimes generated in harbor-like basins by the external potential long shore current at large Reynolds numbers. The proposed theory discusses the issues of what solution compatible with the Prandtl-Batchelor theorem for inviscid fluids, and under what conditions, may be realized as an asymptotic state of the open hydrodynamical system. The analysis developed is based on the variational principle. We formulated a validity criterion according to which stationary regimes of dissipative systems may be considered as extremals of a variational inviscid problem. In particular, such a situation is possible when the dissipative functionals represent some functions of motion invariants of the same problem. It is shown that the steady state corresponds to the circulational regime in which the system has minimal energy with the fixed enstrophy. This state is fixed by the Reynolds number. The approach that is formulated is applied to the model of a rectangular harbor-like basin in order to obtain the relation between the Reynolds number, the geometry factor and the topological number characterizing the number of vortex cells. © 1998 American Institute of Physics.

Notes: Data obtained using the Raman/Rayleigh/LIF technique in turbulent nonpremixed reacting flows behind a bluff-body are analyzed to study the behavior of conditionally averaged temperature and species mass fraction. In particular, their cross stream dependence in the elliptic region of the above flow fields is investigated from the conditional moment closure view. Analyses show that the conditional averages have a very weak dependence on the cross stream position in recirculation regions which are elliptic in nature. The weak cross stream dependence of the conditional averages has been established in previous studies for parabolic flows. © 1998 American Institute of Physics.

Notes: Using dye visualization techniques, we have observed vortex structures within the jet region of round transverse jets which, to the best of our knowledge, have not been reported before. These structures confirm the existence of a pair of negative bifurcation lines in the surface flow of the pipe and the conjecture of Abramovich (1963) concerning additional vortical motions within the jet itself. © 1998 American Institute of Physics.

Notes: An inviscid algebraic instability for streamwise independent disturbances in compressible flow is found to be related to Ellingsen and Palm's [Phys. Fluids 18, 487 (1975)] solution for incompressible flow. For compressible flow, the streamwise disturbance velocity, the density, as well as temperature perturbations grow linearly with time. The effect of viscosity on the inviscid algebraic growth is clarified using a rescaling of the viscous disturbance equations, showing the dependence of the viscous transient growth on the Reynolds number. © 1998 American Institute of Physics.

Notes: The problem of pattern formation in thin liquid films with insoluble surfactants under attractive and repulsive forces is addressed. A thin fluid film bounded by a wall is modeled by a set of two nonlinear evolution equations for the film thickness and surfactant concentration on the free interface. We perform a bifurcation analysis valid for the general case of apolar and polar forces and predict a supercritical bifurcation to new stationary and periodic structures. Numerical simulations for the particular case of a negative apolar spreading coefficient (attractive van der Waals forces) and a positive polar spreading coefficient (repulsive hydration pressure) are discussed in terms of the analytical predictions. Nonlinearities in the competition between attractive and repulsive forces can lead to formation of periodic patterns for the film thickness with homogeneously distributed surfactants. Due to diffusion and Marangoni effects, insoluble surfactants alter the time required for pattern formation but do not alter the final pattern profile itself. Bifurcation analysis allows us then to predict the ranges of film parameters in which pattern formation, rupture, or total film spreading is possible. © 1998 American Institute of Physics.

Notes: Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane–fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated. © 1998 American Institute of Physics.

Notes: The conventional approach to small-scale mixing enhancement in free shear flows by the manipulation of global flow instabilities and the ensuing large-scale vortical structures depends on the classical cascading mechanism to transfer the control influence to the scales at which molecular mixing takes place. Thus the manipulation of mixing at the smallest scales is indirect and only weakly coupled to the control input. The present work focuses on direct excitation of the small scales within the dissipation range of a free shear flow. This approach is demonstrated in a shear layer segment of an air jet emanating from a square conduit. The flow is forced at a frequency that is approximately an order of magnitude lower than the passage frequency of eddies at the Kolmogorov scale using cantilevered piezoelectric actuators. Cross-stream distributions of the streamwise velocity component are measured at a number of streamwise stations downstream of the actuator using hot wire anemometry. Direct small scale excitation results in enhanced energy transfer from the large to the small scales and in a substantial increase in the dissipation and in the decay rate of turbulent kinetic energy. © 1998 American Institute of Physics.

Notes: The concept of conjugate flows is used to determine the vertical structure of solitary internal waves which are horizontally uniform in their center. Continuously stratified fluids are considered and solutions obtained with and without the Boussinesq approximation are compared. Only mode-1 waves are considered. For stratifications with a single pycnocline, conjugate flow solutions are obtained provided the pycnocline is not too close to the upper or lower boundaries. The parallel shear flow in the center of a flat solitary wave is potentially unstable (minimum Richardson number less than 1/4) if the upstream pycnocline is sufficiently narrow. For stratifications with two pycnoclines, cases with three mode-1 conjugate flow solutions have been found. Some conjugate flow solutions for the two-pycnocline case do not seem to correspond to a flat solitary wave. Non-Boussinesq effects were found to be small if the surface to bottom density difference is about 4% for stratifications with one or two pycnoclines. © 1998 American Institute of Physics.

Notes: The nonlinear development of Görtler vortices in a curved compressible mixing layer is studied. It has been shown both experimentally and theoretically that the curved mixing layer can support a centrifugal mode, which is believed to be similar to the Görtler vortex. This study follows the corresponding incompressible study of Seddougui & Otto [Proceedings of the IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, edited by P. W. Duck and P. Hall (Kluwer Academic, Amsterdam, 1995)] and attempts to demonstrate the effect compressibility has on the growth of such modes. The formulation follows that of Hall & Lakin [Proc. R. Soc. London, Ser. A 415, 421 (1988)] for the corresponding incompressible boundary-layer problem, and utilises a stream function formulation to solve the governing equations. We will present the nonlinear structure of the so-called thermal modes, whose linear counterparts were first discovered in Owen, Seddougui & Otto [Phys. Fluids 9, 2506 (1997)]. A brief discussion will be made concerning the effect of the nonlinear modes on the inherent Kelvin–Helmholtz modes of instability, which may have significant ramifications in flows dominated by this form of instability. © 1998 American Institute of Physics.

Notes: A temporal linear stability analysis of an inviscid incompressible gas jet injected into a co-flowing viscous liquid was conducted to study the growth of small three-dimensional disturbances that lead to the break-up of the gas jet. The primary flow parameter that governed the growth of the disturbances was the gas Weber number. At small Weber numbers, only the two-dimensional varicose disturbances were unstable; at high Weber numbers, three-dimensional disturbances became unstable with growth rates comparable to the sinuous and varicose disturbances. The phase velocity of the disturbances in the gas jet was small, on the order of the co-flowing liquid velocity. © 1998 American Institute of Physics.

Notes: To investigate the nature of the forces involved in mechanical contact between fibers in a fluid, the interaction between a polymeric fiber settling under the influence of gravity and a fixed strand of the same material was observed. Initially after impact, the sedimenting fiber rotated about a fixed point. When the fiber came sufficiently close to vertical alignment so that the tangential component of gravity overcame the static friction, it slid along the surface of the fixed strand. The orientation of the fiber and its velocity were measured as a function of time, and compared to a simple model. The static coefficient of friction was found to be 0.38±0.06, in good agreement with published values. However, the velocity of the fiber after the onset of sliding was slower than that predicted by a theory incorporating friction and smooth cylinder lubrication, and an additional velocity-dependent resistance was required to model the fiber's sliding motion. A possible source of this resistance is the coupling of normal and tangential lubrication forces as roughness elements are forced to lift past each other. © 1998 American Institute of Physics.

Notes: Based on experiments a new law is proposed for the vortex shedding from a circular cylinder which describes in a consistent way the Strouhal–Reynolds-number dependency as Sr=Sr*+m/Re from the beginning of the vortex shedding at Re=47 up to the laminar–turbulent transition of the cylinder boundary layer at Re〉2×105. The various vortex shedding processes, occurring with increasing Reynolds number, are described by different coefficients Sr* and m. © 1998 American Institute of Physics.

Notes: Experimental observations of a purely elastic flow instability occurring in the lid-driven cavity flow of two semi-dilute polymer solutions are reported and the effect of cavity aspect ratio on the dynamical structure of the unstable flow is quantitatively investigated. The spatial and temporal characteristics of the secondary flow are measured using flow visualization, laser Doppler velocimetry, and digital particle image velocimetry. At the onset conditions the disturbances appear in the form of spatially periodic flow cells which propagate along the neutral direction of the cavity. The secondary flow structure is analogous to the Taylor–Görtler vortices observed in inertially driven hydrodynamic instabilities. The critical onset conditions for two elastic test fluids and five different aspect ratios correlate with a recently proposed dimensionless stability criterion which incorporates measures of the local streamline radius of curvature and the non-Newtonian normal stresses in the flow domain. © 1998 American Institute of Physics.

Notes: We consider the 2:1 internal resonances (such that Ω1〉0 and Ω2(similar, equals)2Ω1 are natural frequencies) that appear in a nearly inviscid, axisymmetric capillary bridge when the slenderness Λ is such that 0〈Λ〈π (to avoid the Rayleigh instability) and only the first eight capillary modes are considered. A normal form is derived that gives the slow evolution (in the viscous time scale) of the complex amplitudes of the eigenmodes associated with Ω1 and Ω2, and consists of two complex ODEs that are balances of terms accounting for inertia, damping, detuning from resonance, quadratic nonlinearity, and forcing. In order to obtain quantitatively good results, a two-term approximation is used for the damping rate. The coefficients of quadratic terms are seen to be nonzero if and only if the eigenmode associated with Ω2 is even. In that case the quadratic normal form possesses steady states (which correspond to mono- or bichromatic oscillations of the liquid bridge) and more complex periodic or chaotic attractors (corresponding to periodically or chaotically modulated oscillations). For illustration, several bifurcation diagrams are analyzed in some detail for an internal resonance that appears at Λ(similar, equals)2.23 and involves the fifth and eighth eigenmodes. If, instead, the eigenmode associated with Ω2 is odd, and only one of the eigenmodes associated with Ω1 and Ω2 is directly excited, then quadratic terms are absent in the normal form and the associated dynamics is seen to be fairly simple. © 1998 American Institute of Physics.

Notes: Experimental data on differential diffusion between two species with large and quite disparate Schmidt numbers were obtained in a turbulent water jet by optically measuring the two species concentrations simultaneously. Experimental conditions were chosen so that the species were dilute and did not affect the water density thereby avoiding inertial effects. Differential diffusion was found to be significant in magnitude, even in the absence of these effects. Schmidt number ratios of 4 and 18 were considered. Differential diffusion was found to be statistically significant and to manifest at scales larger than the computed Batchelor scale. In some instances the concentration signal for the species with larger diffusivity was simply a blurred version of the other, while in other instances structures present in one signal were completely absent from the other. This second observation, presumably a more complex effect due to diffusion across velocity gradients, is discussed. © 1998 American Institute of Physics.

Notes: Direct numerical simulations were performed in order to investigate the evolution of turbulence in a stably stratified fluid forced by nonvertical shear. Past research has been focused on vertical shear flow, and the present work is the first systematic study with vertical and horizontal components of shear. The primary objective of this work was to study the effects of a variation of the angle θ between the direction of stratification and the gradient of the mean streamwise velocity from θ=0, corresponding to the well-studied case of purely vertical shear, to θ=π/2, corresponding to purely horizontal shear. It was observed that the turbulent kinetic energy K evolves approximately exponentially after an initial phase. The exponential growth rate γ of the turbulent kinetic energy K was found to increase nonlinearly, with a strong increase for small deviations from the vertical, when the inclination angle θ was increased. The increased growth rate is due to a strongly increased turbulence production caused by the horizontal component of the shear. The sensitivity of the flow to the shear inclination angle θ was observed for both low and high values of the gradient Richardson number Ri, which is based on the magnitude of the shear rate. The effect of a variation of the inclination angle θ on the turbulence evolution was compared with the effect of a variation of the gradient Richardson number Ri in the case of purely vertical shear. An effective Richardson number Rieff was introduced in order to parametrize the dependence of the turbulence evolution on the inclination angle θ with a simple model based on mean quantities only. It was observed that the flux Richardson number Rif depends on the gradient Richardson number Ri but not on the inclination angle θ. © 1998 American Institute of Physics.

Notes: There have been many studies of turbulent combustion flows, however the interaction between turbulent motion and the chemical reactions that occur in hypersonic flows has not been studied. In these flows, the rate of product formation depends almost exclusively on the temperature, and small temperature fluctuations may produce large changes in the rate of product formation. To study this process, we perform direct numerical simulations of reacting isotropic turbulence decay under conditions typical of a hypersonic turbulent boundary layer flow. We find that there is a positive feedback between the turbulence and exothermic reactions. That is, positive temperature fluctuations increase the reaction rate, thereby increasing the heat released by the reaction, which further increases the temperature. Simultaneously, the pressure increases causing localized expansions and compressions that feed the turbulent kinetic energy. The Reynolds stress budget shows that the feedback occurs through the pressure-strain term. We also find that the strength of the feedback depends on how much heat is released, the rate at which it is released, and the turbulent Mach number. The feedback process is negative for endothermic reactions, and temperature fluctuations are damped. © 1998 American Institute of Physics.

Notes: A new explanation of the well documented effects of mild streamline curvature on the anisotropy of sheared turbulence has been developed. Its main underlying assumption is that the mean streamline curvature has no direct effect on the production and dynamics of each individual turbulent eddy, which is produced with the structure of purely sheared turbulence, and is subsequently convected downstream while retaining its initial anisotropy relative to fixed inertial coordinates. The local Reynolds stress anisotropy accumulates the contributions of all surviving eddies produced upstream, which, because the mean shear keeps changing direction, have different anisotropies, when viewed in terms of the local curvilinear coordinates; thus, the local anisotropy is influenced by the history of flow curvature only indirectly. A model developed to demonstrate the validity of the hypothesis requires only the specification of the turbulence anisotropies in a fully developed, rectilinear, reference flow (e.g., a rectilinear uniformly sheared flow), the geometrical features of the flow under study, and a dimensionless mean eddy lifetime. It predicts accurately the observed asymptotic turbulence structure of uniformly sheared flow subjected to prolonged, constant curvature and the exponential adjustment of this structure to stepwise changes in flow curvature. Predictions of the shear stress anisotropy in a curved mixing layer are also in good agreement with published data. In all these cases, the present model makes better predictions than two popular Reynolds stress models and a rapid distortion model. © 1998 American Institute of Physics.

Notes: Receptivity and stability of a two-dimensional laminar wall jet is considered. The wall jet and the disturbance source examined in a direct numerical simulation by S. Wernz and H. F. Fasel (AIAA Paper 96-0079) are chosen for the analysis. The disturbances are introduced by blowing and suction through a slot in the wall. The disturbances of two frequencies (28 and 56 Hz) are considered. Because two eigenmodes may be unstable in the wall-jet flow, both of them are taken into account for each frequency. Therefore, the linear receptivity problem is solved for two pairs of eigenmodes, and their development and interaction downstream from the source are analyzed. The analysis allows one to explain the behavior of the fundamental and subharmonic disturbances observed in the numerical simulation. © 1998 American Institute of Physics.

Notes: A dynamic similarity subgrid-scale (SGS) unmixedness model is presented for large eddy simulation (LES) of turbulent reacting flows. The model is assessed both a priori and a posteriori via data obtained by direct numerical simulations (DNS) of homogeneous compressible turbulent flows involving a single step Arrhenius reaction. The results of a priori analysis indicate that the local values of the SGS unmixedness are accurately predicted by the model. A posteriori results also indicate that the statistics of the resolved temperature and scalars as obtained by LES compare favorably with DNS values. © 1998 American Institute of Physics.

Notes: Here we investigate the effect of a steady pressure disturbance moving at a constant velocity along the interface of a thin viscous film flowing down an inclined plane. Both steady and unsteady solutions are determined for the interface. We find that it is possible for the steady solutions to have surface waves, either preceding the disturbance or behind it, depending on the values of the Bond and capillary numbers. In addition, for fixed Bond number, disturbance amplitude, and constant film heights both far upstream and downstream, there exists a finite range of capillary numbers for which no steady solutions exist. Within this range of capillary numbers, the transient solution develops a shock like profile which adjusts the heights upstream and downstream of the disturbance and grows in width. © 1998 American Institute of Physics.

Notes: The heat transfer rate and the hydrodynamic forces experienced by a single vapor bubble of variable radius moving in a superheated or subcooled liquid are studied by means of numerical simulation. For that purpose the full Navier–Stokes equations and the temperature equation are solved in a frame of reference where the bubble surface is steady. The time evolution of the bubble radius is determined by solving the energy balance at the bubble surface. The numerical method is first validated by comparing present predictions with previous asymptotic or numerical results in the case where no relative motion between the liquid and the bubble exists. Then the situation where a constant relative velocity exists is considered. Effects of the mean flow on the heat transfer rate and on the bubble radius evolution are first discussed. Two different stages are generally observed in the computations. First, the radial motion induced by the displacement of the bubble surface dominates and the bubble evolution is essentially identical to the one observed in a liquid at rest. Then the ratio between the radial velocity and the translatory velocity decreases and the heat transfer rate becomes governed by streamwise advection effects. In this second stage a substantial increase of the growth or collapse rate of the bubble is observed, compared to the case of a liquid at rest. For a growing bubble it is shown that the complete process is successively described by the analytical solutions given by Scriven [Chem. Eng. Sci. 10, 1 (1959)] and Rückenstein [Chem. Eng. Sci. 10, 22 (1959)]. The situation is much less simple for a collapsing bubble and the reasons of this increased complexity are discussed. It is found that, when the heat transfer mechanism is dominated by streamwise advection, the bubble evolution and the collapse time predicted by the simulations agree well with the experimental results obtained by Chen and Mayinger [Int. J. Multiphase Flow 18, 877 (1992)]. Based on the present results, a general correlation giving the collapse time as a function of the characteristic parameters of the problem is proposed. The second contribution of the present work concerns the hydrodynamic force experienced by the bubble. Using a general decomposition procedure, the added mass effect and the viscous contribution are separately identified. It is first shown that the added mass coefficient is strictly constant and equal to one half, whatever the Reynolds number and the relative magnitude of the radial velocity. The viscous drag is then systematically compared with the quasisteady viscous drag corresponding to the instantaneous value of the Reynolds number. In situations of boiling, effects due to unsteadiness are found to exist during the first stages of the motion if the initial Reynolds number is not very large. In contrast, for a collapsing bubble, such effects remain significant all along the process because the relative importance of viscous phenomena increases in time. In both cases it is shown that the time variations of the bubble radius may affect deeply the viscous drag force. For example, when the radial velocity is high enough, the viscous drag force is found to be identical to the one corresponding to a potential flow, even if the instantaneous Reynolds number is low. These effects are discussed with the help of two asymptotic expressions of this force derived recently by Magnaudet and Legendre [Phys. Fluids 10, 550 (1998)] for a bubble with a time-dependent radius. © 1998 American Institute of Physics.

Notes: A Revised Enskog theory, valid to second order in the Enskog approximation, is used to characterize the amount of thermal diffusion in a steady, fully developed flow of a binary mixture of hard, inelastic spheres. The dependence of the thermal diffusion factor on mixture volume fraction, mole fraction, radii ratio, and material density ratio is explored in the presence and absence of gravity. © 1998 American Institute of Physics.

Notes: The impact of a drop on a solid surface generates a rapidly expanding thin jet traveling along the surface. We study the evolution of the fingering pattern at the edge of this jet during the impact of a water drop on a glass plate. Multiple-flash photography shows that systematic changes in frontal shapes take place during the expansion. The initial fingers widen and split in two. This splitting is in many cases limited to the development of a double peak on each finger. The subsequent interaction of two such adjacent undulations often results in merging which produces three pronounced fingers. Despite the significant changes in the frontal shapes, the number of fundamental undulations remains approximately constant during the expansion. The progenitors of these azimuthal disturbances are observed right at first contact. Some heuristic arguments based on capillary waves are put forth to explain the splitting and merging. The main focus of this study is on impacts having Reynolds numbers of about 15 000, based on the drop diameter. The corresponding Weber numbers are about 1000. © 1998 American Institute of Physics.

Notes: The nonlinear interaction of two disturbances excited successively in a two-dimensional Couette flow is shown to lead to a transient energy growth. This phenomenon, which is called the echo effect and exists in several other physical systems, is interesting because the energy growth appears long after the energy associated with the original disturbances has decayed. Here, the echo effect is studied analytically and numerically in a situation where the nonlinear response has the same order of magnitude as the two excitations. A system of amplitude equations describing the nonlinear interactions between three sheared modes is derived and employed to examine the physical mechanism of the echo. The qualitative validity of this system is confirmed by numerical simulations. The influence of viscous dissipation on the echo effect is also considered. © 1998 American Institute of Physics.