Numerical study of Rayleigh-Taylor instability between miscible fluids with spectral element method

Abstract

Rayleigh-Taylor instabilities between miscible fluids are studied with a specially-developed unsteady three-dimensional high order spectral element method code. The numerical model used in this code consists of Navier-Stokes equations and a transport-diffusive equation, and the code is validated with results of linear stability perturbation theory. Several characteristics of the Rayleigh-Taylor instabilities are studied including: instantaneous turbulent structures, and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that the spectral element method should provide the capability of simulating small scale fluctuations in Rayleigh-Taylor instabilities turbulent flows.