Effects of Atwood number and stratification parameter on compressible multi-mode Rayleigh–Taylor instability

Abstract

This study numerically analyzes the two-dimensional (2D) compressible multi-mode Rayleigh–Taylor instability at different Atwood numbers (At) and stratification parameters (Sr), corresponding to the different levels of flow compressibility. It is found that the growth of bubble thickness is suppressed with the increase in Sr due to the density stratification at small At, whereas it is enhanced at large At, because of the expansion and compression motions. The ratio of the bubble to spike thickness increases with the increase in Sr at any At. The effects of the flow compressibility on the molecular mixing fraction, Taylor Reynolds number, turbulent Mach number, and velocity divergence statistics are similar at different Atwood numbers. The expansion and compression motions are enhanced by increasing the Sr and At. The expansion motions are relatively strong in the mixing layer, whereas the compression motions are prevalent outside the mixing layer, which may form a force promoting the upward movement of the bubble. The profiles of mean concentration, mean temperature, and root mean square of velocities can overlap with each other at different stratification parameters after normalization, which demonstrates the self-similarity of the 2D compressible Rayleigh–Taylor (RT) turbulence. The density stratification weakens the conversion from potential energy to kinetic energy, while the flow compressibility enhances the pressure-dilatation work at large values of Sr. The present results can help in the development of theoretical models of compressible RT turbulence.