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

TL;DR

This paper investigates how viscosity and surface tension influence the nonlinear development of fluid interfacial structures caused by Rayleigh-Taylor and Richtmyer-Meshkov instabilities, highlighting their roles in suppressing growth and altering spike behavior.

Contribution

It provides a detailed analysis of the effects of viscosity and surface tension on nonlinear interfacial structures, including new insights into spike dynamics and the suppression of growth rates.

Findings

Viscosity and surface tension suppress bubble growth.

Viscosity makes spike velocity tend toward terminal.

Results align with previous simulations and theoretical models.

Abstract

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.