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  • 1
    Electronic Resource
    Electronic Resource
    Book reviews (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 502-503 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945936
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  • 2
    Electronic Resource
    Electronic Resource
    Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2738-2762 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Sideband instabilities following the onset of traveling interfacial waves in two-layer Couette–Poiseuille flow are considered. The usual Ginzburg–Landau equation does not apply to this problem due to the presence of a long-wave mode for which the decay rate tends to zero in the limit of infinite wavelength. Instead of the Ginzburg–Landau equation, a coupled set of equations for three amplitude factors is derived. The first corresponds to an amplitude of a traveling wave, the second to a long-wave modulation of the interface height, and the third results from the pressure. The criteria which determine the stability of the primary traveling wave to sideband perturbations are presented. This scenario raises the possibility that as a result of sideband instability of a primary traveling wave, the flow may eventually be dominated by a long-wave mode. Experimental data on a gas–liquid flow are analyzed and models for air–water waves are discussed. Finally, it is noted that the amplitude equations allow for possibilities other than periodically modulated waves. In the concluding section, the presence of homoclinic and heteroclinic orbits is investigated. These correspond to solutions which approach either a flat interface or periodic waves at infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858737
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  • 3
    Electronic Resource
    Electronic Resource
    Erratum: "Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows'' [Phys. Fluids A 5, 2738 (1993)] (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3502-3502 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868407
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 269-282 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volume-of-fluid (VOF) method. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds number. Our simulations compare well with previous theoretical, numerical, and experimental results. For capillary numbers greater than the critical value, the drop deforms to a dumbbell shape and daughter drops detach via an end-pinching mechanism. The number of daughter drops increases with the capillary number. The breakup can also be initiated by increasing the Reynolds number. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870305
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  • 5
    Electronic Resource
    Electronic Resource
    Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 2699-2708 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In a recent paper, Renardy and Joseph [Phys. Fluids 28, 788 (1985)] studied the Bénard problem for two layers of different fluids lying on top of each other and bounded by walls. Their study shows that, in contrast to the Bénard problem for one fluid, the onset of instability can be oscillatory. The number of parameters involved in the problem is large, and there is as yet no comprehensive picture of when the instability is oscillatory and when it is not. The study of limiting cases, accessible by perturbation methods, may be helpful in this respect. In this paper, an analysis is given for the case when the properties of the two fluids are nearly equal and the fluids are allowed to slip at the boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865227
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  • 6
    Electronic Resource
    Electronic Resource
    A numerical study of periodic disturbances on two-layer Couette flow (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 3056-3071 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869834
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  • 7
    Electronic Resource
    Electronic Resource
    Energy methods for a parabolic-hyperbolic interface problem arising in electromagnetism (1988)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 931-936 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Wir betrachten ein zweidimensionales Problem, welches bei der Wechselwirkung einer sich in Luft ausbreitenden elektromagnetischen Welle mit einem metallischen Objekt auftritt. Dieses Problem führt auf eine parabolische Gleichung innerhalb des Objekts und eine hyperbolische Gleichung außerhalb; die beiden Gleichungen sind durch Sprungbedingungen an der Grenzfläche gekoppelt. Wir zeigen die Existenz von Lösungen mittels Energieabschätzungen in Verbindung mit einem Galerkin-Argument. Es wird auch angedeutet, wie man ähnliche Resultate im dreidimensionalen Falle erhält.
    Notes: Abstract We consider a two-dimensional problem arising from the interaction of electromagnetic waves traveling in air with a metallic body. This problem leads to a parabolic equation inside the body and a hyperbolic equation outside; the two equations interact through jump relations across the boundary of the body. We prove the existence of solutions using energy estimates in conjunction with a Galerkin argument. We also remark on how to obtain similar results in the three-dimensional case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945129
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  • 8
    Electronic Resource
    Electronic Resource
    On an eigenvalue problem arising in the study of the stability of ocean currents (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 497-501 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study a singular Sturm-Liouville eigenvalue problem which arises in studying the stability of rotating shallow-water shear flows on an equatorial β-plane. Earlier studies have shown that the problem has only stable eigenvalues if a certain parameter φ exceeds 3/4. On the other hand, numerical studies have found unstable eigenvalues if φ is sufficiently small. In this note, we give an analytical proof that the bound of 3/4 is indeed sharp, i.e. there are instabilities for any φ 〈 3/4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945934
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  • 9
    Electronic Resource
    Electronic Resource
    On the linear stability of hyperbolic PDEs and viscoelastic flows (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 854-865 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The issue addressed in this paper is whether linear stability can be determined from the spectrum. We present a counterexample for a hyperbolic PDE in two dimensions and a positive result for parallel shear flows of a class of viscoelastic fluids.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00952081
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  • 10
    Electronic Resource
    Electronic Resource
    Book reviews (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 992-994 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00952091
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