Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    An asymptotic theory for the nonlinear instability of antiparallel pairs of vortex filaments (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 369-379 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Simplified asymptotic equations describing the nonlinear dynamics of perturbed pairs of parallel vortex filaments are derived and analyzed here. The derivations are general enough to allow for vortices of unequal strength, but emphasis here is on the antiparallel vortex pair. The simplified asymptotic equations account for both the internal effects of self-induction and self-stretching for each filament and also the external effects of mutual induction that lead to a nontrivial coupling of the perturbations of the two filaments. When these nonlinear equations are linearized at the unperturbed filament pair, the linearized stability theory of Crow [AIAA J. 8, 2172 (1970)] is recovered in a systematic fashion. The asymptotic equations are derived in a novel singular limit at high Reynolds numbers through assumptions similar to the authors' recent theories [Physica D 49, 323 (1991); ibid. 53, 267 (1991); Phys. Fluids A 4, 2271 (1992)] for the dynamics of a single perturbed vortex filament. Through the Hasimoto transform [J. Fluid Mech. 51, 477 (1972)], these equations become two coupled perturbed nonlinear Schrödinger equations for a pair of filament functions. A series of numerical solutions of the asymptotic equations exhibits several new phenomena in the nonlinear instability of pairs of antiparallel vortex filaments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858860
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields (1997)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 7 (1997), S. 39-48 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Monte Carlo methods for computing various statistical aspects of turbulent diffusion with long range correlated and even fractal random velocity fields are described here. A simple explicit exactly solvable model with complex regimes of scaling behavior including trapping, subdiffusion, and superdiffusion is utilized to compare and contrast the capabilities of conventional Monte Carlo procedures such as the Fourier method and the moving average method; explicit numerical examples are presented which demonstrate the poor convergence of these conventional methods in various regimes with long range velocity correlations. A new method for computing fractal random fields involving wavelets and random plane waves developed recently by two of the authors [J. Comput. Phys. 117, 146 (1995)] is applied to compute pair dispersion over many decades for systematic families of anisotropic fractal velocity fields with the Kolmogorov spectrum. The important associated preconstant for pair dispersion in the Richardson law in these anisotropic settings is compared with the one obtained over many decades recently by two of the authors [Phys. Fluids 8, 1052 (1996)] for an isotropic fractal field with the Kolmogorov spectrum. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166239
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Nonlinear instability of elementary stratified flows at large Richardson number (2000)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 10 (2000), S. 3-27 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319–350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin–Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166472
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1963-1970 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent experimental and computational observations demonstrate the occurrence of large-scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large-scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection–diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher-order statistics for the scalar in these models are solved exactly by formulas for the quantum-harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858823
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic equations for the stretching of vortex filaments in a background flow field (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2271-2281 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recently, two of the authors have derived [Physica D 49, 323 (1991)] and analyzed [Physica D 53, 267 (1991)] a new asymptotic equation for the evolution of small-amplitude short-wavelength perturbations of slender vortex filaments in high Reynolds number flows. This asymptotic equation differs significantly from the familiar local self-induction equation in that it includes some of the nonlocal effects of self-stretching of the filament in a simple fashion. Here, through systematic asymptotic expansions, the authors derive a modification of this asymptotic equation that incorporates the important additional effects of strain and rotation from a general background flow field. The main requirement on the background flow is that it does not displace the unperturbed background filament. The new asymptotic equations exhibit in a simple fashion the direct competition in filament dynamics between internal effects such as self-induction and self-stretching and external effects of background flows involving strain and rotation. Solutions of these asymptotic equations revealing various aspects of this competition are analyzed in detail through both theory and numerical simulation. An application is also presented for the nonlinear stability of a columnar vortex to suitable perturbations in a straining, rotating, background environment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858467
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Nonlinear kink modes for supersonic vortex sheets (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 583-596 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Both recent large-scale numerical simulations and time-dependent asymptotic nonlinear wave theories reveal the prominence of kink modes in the nonlinear instability of supersonic vortex sheets. These kink modes are nonlinear traveling waves that move along the vortex sheet at various speeds and have a wave structure consisting of a kink in the slip stream bracketed by shocks and rarefactions emanating from each side of the kink. Here an explicit construction is developed for calculating all the nonlinear kink modes that bifurcate from a given unperturbed contact discontinuity. This construction is applied at small amplitudes to provide a completely independent confirmation of the asymptotic nonlinear wave theories through a static bifurcation analysis. For the unperturbed vortex sheet, bifurcation diagrams at large amplitudes are also computed for several interesting density ratios and Mach numbers. These results are applied at large amplitude to explain some of the phenomena observed in numerical simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857427
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Crude closure dynamics through large scale statistical theories (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 3431-3442 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Crude closure algorithms based on equilibrium large scale statistical theories involving only a few constraints are developed here. These algorithms involve the nonlinear evolution of either a single parameter, the energy, for dynamic closure based on equilibrium energy-enstrophy statistical theory, or two parameters, the energy and circulation, for crude dynamic closure based on the equilibrium point vortex statistical theory. The crude closure algorithms are tested systematically through numerical experiments with the Navier–Stokes equations in two dimensions on a rectangular domain with stress-free boundary conditions and strong small scale forcing at moderately large Reynolds numbers. A series of successively more stringent tests is devised with conditions ranging from freely decaying flows to spin-up from rest by random forcing with like signed vortices, and finally to random forcing by vortices with alternating or opposite signs. Comparison of standard spectral simulations with crude dynamic closure based on the two-parameter theory yields at most 5% velocity errors for all of these examples. The velocity errors can be as large as 10% for the one-parameter closure theory but are often comparable to those obtained with the two-parameter closure. The results of numerical experiments with Ekman drag are also discussed here. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869453
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Model dynamics and vertical collapse in decaying strongly stratified flows (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 2932-2940 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent laboratory experiments with decaying strongly stratified grid turbulence at moderate Reynolds numbers reveal remarkable behavior. These experiments document the evolution of an initial sea of columnar dipole vortex pairs with dominant vertical vorticity to stratified "pancake" vortex sheets with dominant horizontal vorticity, together with a concurrent dominance of vertical dissipation of kinetic energy as compared with horizontal dissipation. Here we build exact solutions of the equations for low Froude number limiting dynamics, which capture basic qualitative features observed in the above experiments. Unlike the actual turbulent experiments, these exact solutions are laminar and do not involve a cascade of many scales in the horizontal. The exact solutions of the limiting dynamics involve a periodic array of dipole vortices in a weakly vertically sheared horizontal flow. The effect of finite Rossby numbers on the collapse of these exact solutions is also described here. At moderately large Rossby numbers, the effect of rotation is to inhibit the vertical collapse process. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869405
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Singular front formation in a model for quasigeostrophic flow (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 9-11 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A two-dimensional model for quasigeostrophic flow which exhibits an analogy with the three-dimensional incompressible Euler equations is considered. Numerical experiments show that this model develops sharp fronts without the need to explicitly incorporate any ageostrophic effect. Furthermore, these fronts appear to become singular in finite time. The numerical evidence for singular behavior survives the tests of rigorous mathematical criteria.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868050
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Approximate and exact renormalization theories for a model for turbulent transport (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 41-57 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The capability of renormalization group methods (RNG) and Lagrangian renormalized perturbation theories (RPT) to reproduce a renormalized theory of eddy diffusivity for turbulent transport diffusion is discussed in the context of a simplified model with an exact renormalization theory that has recently been developed by the authors. The model problem involves transport diffusion by simple shear flows with turbulent velocity statistics, infrared divergences, and no separation of scales; the exact renormalization theory exhibits a remarkable range of different phenomena as parameters defining the velocity statistics are varied with four distinct regions requiring renormalization so that the model is a stringent test for approximate theories of eddy diffusivity via either RNG or RPT methods. Despite the different philosophy in RNG and RPT methods, all of these different approximations collapse to give the exact theory of eddy diffusivity for one region in the model with infrared divergence that is adjacent to the Kolmogorov value. The RNG methods are very flexible but do not give the exact anomalous scaling exponents for the other three regions with infrared divergence as expected with an ε-expansion procedure. The Lagrangian RPT methods always yield the correct scaling exponents but a much more elaborate analysis of the explicit structure of the model problem is needed to achieve this. In other regions of renormalization, including the Kolmogorov value, the RPT methods predict nonlocal equations for eddy diffusivity while the exact renormalization theory involves local diffusion equations with time-dependent diffusivity; these nonlocal equations are a poor approximation for the actual renormalized dynamics and the Lagrangian direct interaction approximation (DIA) only slightly improves the behavior over the Lagrangian first-order smoothing approximation. On the other hand, RNG methods alway predict a simple local diffusivity in the model and there are regions of renormalization where the rigorous theory for eddy diffusivity is nonlocal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858499
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...