Transition to turbulence in horizontally-sheared stratified Kolmogorov flows

While the transition to turbulence of vertically-sheared stratified flows is now relatively-well understood, their horizontally-sheared counterparts have received considerably less attention. Yet, horizontal shear instabilities remain active even when the Richardson number is large or infinite, and can drive stratified turbulence at sufficiently high Reynolds number. If the background flow is vertically-invariant, the onset of turbulence requires breaking the vertical symmetry to generate three-dimensional motions. The central question, then, is how this symmetry breaking occurs. In this work, we combine linear theory with DNS to investigate the transition to turbulence in a strongly stratified non-rotating horizontally-sheared Kolomogorov flow. We identify two distinct pathways to turbulence, that depend on the initial conditions selected. In the first pathway, the horizontal shear instability first induces vertically-invariant meanders in the flow, which evolve into columnar vortices. These vortices are subsequently unstable to small-scale three-dimensional hyperbolic instabilities. In the second pathway, the horizontal shear instability is modulated in the vertical direction. This modulation introduces vertical shear, which in turns triggers localized Kelvin-Helmholtz instabilities when and where the Richardson number drops below 1/4. These two routes to turbulence have significantly different peak mixing efficiencies.