Role of unstable thermal stratifications on the Rayleigh–Taylor instability

Abstract

Three-dimensional simulations of Rayleigh–Taylor instability (RTI) at the interface of two masses of air are performed by solving the compressible Navier–Stokes equation, following the numerical implementation in Role of non-zero bulk viscosity in three-dimensional Rayleigh–Taylor instability: Beyond Stokes’ hypothesis - Sengupta et al. (2021). The effect of thermal gradients on the RTI is explored by considering two temperature differences between the air masses, ΔT=21.75K and 46.5K, corresponding to Atwood numbers (At) of 0.035 and 0.073. The flow is studied in an isolated box with non-periodic walls along three directions. A non-conducting interface, initially separating the two air masses, is removed at the onset of the numerical experiment. The stages in the evolution of the RTI are explored via the enstrophy transport equation (ETE). The contributions from vortex stretching, viscous diffusion and dissipation are quantified for different thermal gradients, showing completely different dynamics. For both At considered, the viscous dissipation term is found to dominate across the stages of RTI evolution, with vortex stretching becoming prominent beyond the development of spikes and bubbles in the mixing layer. For At=0.035, two interpenetrating rows of bubbles are noted, whereas, for At=0.073, an alternating row of bubbles and spikes are noted with a 19% rise in the growth rate of the mixing layer. The present simulations have been experimentally validated for a combined Kelvin–Helmholtz Rayleigh–Taylor instability (KHRTI). It is found that the vortical structures, representative of the KH instability, are stretched and diffused due to the buoyancy-driven RT mechanism.