Kelvin–Helmholz instability in thermoviscous free shear flow

Abstract

This paper is focused on the entrainment and mixing in the nonisothermal shear flow, wherein the velocity profile discontinuity arises due to viscosity–temperature relation, i.e. thermoviscosity. Kelvin–Helmholz instability generated at the interface paves the way to large-scale entrainment which is analysed in terms of perturbation growth rate and momentum thickness. The flow is simulated in the plane domain with periodic boundary conditions using second-order accuracy explicit CABARET numerical scheme in weakly compressible formulation. Initial instability evolution is fully governed by a universal scaling parameter kt, composed of Reynolds number Re and kinematic viscosity ratio Rν. There are seven flow configurations determined by nonlinear mode interaction, vorticity convection and diffusion and cascade vortex merger. The problem at issue appears to be analogues to the classical boundary layer theory that totally fortifies its remarkable features.