Thermally stratified free shear layers: Combined Kelvin–Helmholtz Rayleigh–Taylor instability

Abstract

A numerical investigation of Rayleigh–Taylor instability (RTI) with different unstable thermal stratifications, and coupled Kelvin–Helmholtz (KH) and RTI (referred to as KHRTI) is performed by solving the compressible Navier–Stokes equation. Two air masses having temperature differences of ΔT*=21.75 and 46.5 K [corresponding to Gay–Lussac numbers (Ga) of 0.073 and 0.156] are considered in an isolated box, initially separated by a non-conducting interface for studying RTI. For KHRTI, dimensionless tangential shear of ΔU=0.92 and 1.89 is additionally imposed on the two air masses with ΔT*=21.75 K. Onset propagation and fully developed stages of the instabilities are explored via time-resolved and instantaneous temperature and vorticity. For RTI, lower ΔT* case shows retarded growth of the mixing layer and a set of interpenetrating bubbles. The higher ΔT* case shows an accelerated growth of the mixing layer with alternating rows of spikes and bubbles. For KHRTI, flow is governed by KH dynamics at early times and RT dynamics at later times. To further understand the interaction between RT and KH mechanisms, a compressible enstrophy transport equation in Suman et al. [“A novel compressible enstrophy transport equation based analysis of instability of Magnus–Robins effects for very high rotation rates,” Phys. Fluids 34, 044114 (2022)] is used. Depending on Ga, either vortex stretching or compressibility contribution terms of the enstrophy transport are dominant for RTI. Depending on the shear imposed, either baroclinic torque or viscous terms are dominant for KHRTI.