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A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Parhia, S and Nath, G (1991) A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow. In: International Journal of Engineering Science, 29 (11). 1439-1450 .

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Official URL: http://dx.doi.org/10.1016/0020-7225(91)90049-9


Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Item Type: Journal Article
Publication: International Journal of Engineering Science
Publisher: Elsevier science
Additional Information: Copyright of this article belongs to Elsevier science.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Nov 2010 08:36
Last Modified: 09 Nov 2010 08:36
URI: http://eprints.iisc.ac.in/id/eprint/33635

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