Effects of viscosity on the growth of Rayleigh–Taylor instability

Abstract

Using Zufiria's potential flow model with a point source in the velocity potential, we investigate the effects of viscosity on the growth of the bubble in Rayleigh–Taylor instability. The nonlinear asymptotic solutions are obtained analytically for the velocity and curvature of the bubble. We find that the viscosity decreases the velocity but does not affect the curvature of the bubble, consistent with Sohn's results based on Layzer's potential flow model without a point source in the velocity potential. Furthermore, the dependences of the bubble velocity on the Reynolds number and the Atwood number are studied and we find that both models give the same results at high Reynolds numbers and low Atwood numbers, but smaller velocities are found in Zufiria's model at low Reynolds numbers and high Atwood numbers. Finally, evolution of the velocity with time is studied and the results based on Zufiria's model are found to be in better agreement with recent experimental data than that based on Layzer's model.