Departmental Papers (MEAM)

Document Type

Journal Article

Date of this Version

4-3-1985

Comments

Suggested Citation:
Hogan, J.M. and Portonovo S. Ayyaswamy. (1985) Linear stability of a viscous-inviscid interface. Physics of Fluids. Vol. 28(9).

Copyright 1985 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

The following article appeared in Physics of Fluids and may be found at http://link.aip.org/link/PFLDAS/v28/i9/p2709/s1

Abstract

In this paper the stability of the interface separating fluids of widely differing viscosities has been examined. It is shown that a viscous-inviscid (V-I) model offers a consistent zeroth-order approximation to the stability problem. The zeroth-order solution is obtained by neglecting the smallest-order effect, viz., viscosity on the less viscous side of the interface. In this sense, the V-I model significantly differs from the Kelvin-Helmholtz (K-H) approach where both the viscosities are dropped in a single step. A closed form solution for the stability criterion governing the V-I model has been obtained, and a novel instability mechanism is described. It is shown that the V-I model is also a consistent zeroth-order approximation for the Rayleigh-Taylor problem of a viscous-viscous, nonflowing interface when the viscosity ratio tends to zero. For the interface separating two viscous, nonflowing, incompressible fluids, exact solutions for the velocities, pressures, and interface displacement for a disturbance of a given wavelength have been provided for the stable (lighter fluid on top) wave motion. By discussing the roles played by the dynamic and kinematic viscosities, it is made clear why neither the V-I nor the K-H model should apply to the air-water interface. The results of the V-I model compare well with experimental observations. The V-I model serves as an excellent basis for comparison in detailed numerical studies of the viscous-viscous interface.

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Date Posted: 17 August 2010

This document has been peer reviewed.