Effect of viscosity and surface tension on the growth of Rayleigh -Taylor instability and Richtmyer-Meshkov instability induced two fluid inter-facial nonlinear structure

The effect of viscous drag and surface tension on the nonlinear two fluid inter facial structures induced by Rayleigh -Taylor instability and Richtmyer-Meshkov instability are investigated.Viscosity and surface tension play important roles on the fluid instabilities. It is seen that the magnitude of the suppression of the terminal growth rate of the tip of the bubble height depends only on the viscous coefficient of the upper (denser) fluid through which the bubble rises and surface tension of the interface. But in regard to spike it is shown that in an inviscid fluid spike does not remain terminal but approaches a free fall as the Atwood number A increases. In this respect there exits qualitative agreement with simulation result as also with some earlier theoretical results. Viscosity reduces the free fall velocity appreciably and with increasing viscosity tends to make it terminal. Results obtained from numerical integration of the relevant nonlinear equations describing the temporal development of the spike support the foregoing observations.