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The effect of magnetic field and compressibility on the Rayleigh - Taylor instability

Vijayalakshmi A. R.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 3

899-910

The Rayleigh-Taylor instability of inviscid electrically conducting compressible fluid layer of finite thickness in the presence of magnetic field has been investigated. The linear growth rate for the instability that occurs when the density in the region above the interface is greater than that of fluid below is calculated by solving the linear eigenvalue problem obtained using the normal mode analysis. This problem has been solved separately in both the regions which are filled with constant temperature ideal polytrope exponentially stratified electrically conducting fluids and the eigenfrequencies are obtained by using the kinematic and dynamic pressure matching conditions at the interface. Thus we have obtained the solution of the eigenvalue problem for the frequencies and investigated its dependence on the wave number k and other parameters. We have also obtained various limiting cases viz when the wave number k - 0 and the adiabatic index [...]. For finite y i.e., compressible fluids, it is observed that the growth rates are greater than that for the incompressible fluids. It is also observed that the growth rate decreases with magnetic field. Numerical results are obtained and the limiting cases are deduced which illustrate the importance of the general nature of the problem and the conclusions.

Rayleigh-Taylor instability in a finite thickness layer of a non-Newtonian fluid

Rudraiah N., Sridharan P., Bhargava S.

Applied Mechanics and Engineering

2000

Vol. 5, no 2

315-327

A mechanism of surface instability in non-Newtonian fluid is described using Rayleigh-Taylor instability as an example. The combined effects of non-Newtonian parameter n, normal stress 'delta', film thickness h, and surface tension 'gamma' on surface instability is studied using linear stability analysis. It is shown that stable, neutrally stable and unstable states are possible depending on the values of n, in contrast to the existence of only unstable state in Newtonian fluids. Further, the graph of dispersion curve reveals that both n and 'lambda'(='gamma'/'delta') control dispersion curve with the layer thickness just affecting the nature of growth rate of instability.