Stratified turbulent mixing in oscillating shear flows

Motivated by the variation of local shear produced by internal waves in the ocean, we use direct numerical simulations to investigate the effect of a time-dependent shear forcing on the evolution and mixing of turbulence produced by Kelvin–Helmholtz instability (KHI) at high Reynolds number. The forcing is implemented using a tilting coordinate system which causes the background shear to accelerate and decelerate periodically. We demonstrate that, with suitable timing between development of instability and the shear oscillation cycle, turbulence produced by KHI with a decelerating shear mixes in a distinctly different way from the flow with constant background shear, specifically with the energy for turbulent motions extracted from alternative sources. As a result, the total amount of mixing as measured by the change in background potential energy can in fact be significantly larger for flows in which the shear is decelerated, despite the fact that the total kinetic energy in the flow is significantly smaller. The mixing has characteristics more in common with convectively driven rather than shear-driven flows, supporting the argument for an underlying change in the mechanisms triggering the turbulence.