Effects of stabilizing and destabilizing thermal gradients on reversed shear-stratified flows: Combined Kelvin–Helmholtz Rayleigh–Taylor instability

Abstract

Numerical investigation of the coupled Kelvin–Helmholtz Rayleigh–Taylor instability (KHRTI) is presented here by solving the compressible Navier–Stokes equations for two air streams differentially heated in two halves of a three-dimensional (3D) box. Here, we explore the role of a stabilizing and destabilizing thermal gradient and that of reversing the direction of the air streams considered for Atwood numbers of ±0.1567 and dimensionless tangential shear of ΔU=0.68 and 4.1. The onset of the KHRTI and development of the turbulent mixing layer are explored via time-resolved and instantaneous distributions of temperature and vorticity. Early stages of the KHRTI with reversed air streams follows a Kelvin–Helmholtz (KH) mechanism, with Rayleigh–Taylor (RT) dynamics becoming important at later times. This leads to an earlier development of the turbulent mixing layer. The KHRTI with stabilizing or destabilizing thermal gradients shows a dominance of the buoyancy-driven mechanism, right from the onset. The transition from laminar to turbulent mixing layer involves the creation of coherent structures of spikes, bubbles, and KH whirls for the destabilizing, stabilizing thermal gradient, and reversed shear cases, respectively. The spectra of the turbulent signals reveal a −5/3 scaling when the shear-driven mechanism is prevalent in the flow and −11/5 scaling when the buoyancy-driven effects become prominent. The compressible enstrophy budget of the KHRTI shows that the onset process is dominated by vortex stretching or compressibility effects, followed by a sharp rise in baroclinic torque contribution once the buoyancy effects become relevant.