Effect of surface tension on the Rayleigh-Taylor and Richtmyer-Meshkov instability induced nonlinear structure at two fluid interface and their stabilization

Abstract

The effect of surface tension on the Rayleigh-Taylor (RT) instability and Richtmyer – Meshkov (RM) instability induced development of nonlinear structures like spike and bubble at two fluid interface have been investigated. In case of RT instability, the surface tension reduces the velocity of the tip of both the bubble and the spike by the factor (1-k2 /3 kc2) where, k2c = (ρh-ρl)g/T. For k2 > 3 kc2, RT instability is stabilized. Any perturbation, whatever be its magnitude, results in stable large amplitude nonlinear oscillations. The RM instability is always stabilized by surface tension leading to nonlinear oscillation. Both the amplitude and the period of oscillation decreases monotonically as S = 12k2T / (ρh+ρl) increases where k is the wave number. The maximum height attained by the peak of the nonlinear interfacial structures (spike or bubble) increases approximately logarithmically with the initial interface velocity resulting from the shock.