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Viscosity effect on the longwave instability of a fluid interface subjected to horizontal vibrations

Published online by Cambridge University Press:  02 February 2017

D. V. Lyubimov ,
G. L. Khilko ,
A. O. Ivantsov  and
T. P. Lyubimova
D. V. Lyubimov
Affiliation:
Theoretical Physics Department, Perm State University, Perm 614990, Russia
G. L. Khilko
Affiliation:
Laboratory of Computational and Hydrodynamics, Institute of Continuous Media Mechanics UB RAS, Perm 614013, Russia
A. O. Ivantsov
Affiliation:
Theoretical Physics Department, Perm State University, Perm 614990, Russia Laboratory of Computational and Hydrodynamics, Institute of Continuous Media Mechanics UB RAS, Perm 614013, Russia
T. P. Lyubimova*
Affiliation:
Theoretical Physics Department, Perm State University, Perm 614990, Russia Laboratory of Computational and Hydrodynamics, Institute of Continuous Media Mechanics UB RAS, Perm 614013, Russia
*
†Email address for correspondence: [email protected]
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Abstract

The effect of viscosity on the longwave Kelvin–Helmholtz instability of two immiscible incompressible fluids under horizontal vibrations is considered. The linear stability boundaries are found analytically using series expansion in terms of small wavenumber. The values of parameters, at which a transition from the longwave to finite-wavelength instability takes place, are determined. It has been shown that for high-frequency vibrations a viscous dissipation has just a weak destabilizing effect. At vibrations of moderate frequencies, destabilization is more significant, especially in the systems with large viscosity contrast. In contrast to that, at low frequencies the viscosity stabilizes the basic flow by suppressing the longwave perturbations.

JFM classification

Instability: Instability Multiphase and Particle-laden Flows: Multiphase flow Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 814 , 10 March 2017 , pp. 24 - 41
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Copyright
© 2017 Cambridge University Press 

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References

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