Early onset of secondary shear instability in Kelvin-Helmholtz braids at high Reynolds number
We study the onset of two-dimensional secondary shear instability (SSI) in the braid regions connecting primary Kelvin-Helmholtz billows in stratified shear flows. While strain induced by the billows stabilises the braids, it also compresses their tilted isopycnals, enhancing baroclinic shear that enables rapid perturbation growth. By modifying the classical analysis of Corcos & Sherman (J. Fluid Mech. 73, 241-264, 1976) in braid-aligned coordinates and adding an additional stability criterion based on the ratio of strain rate to shear, we develop an inviscid, time-dependent model for the braid and the onset of SSI. We show that the criterion for instability can be achieved significantly earlier than the saturation of the primary billow at sufficiently high initial Richardson number Ri, as increased stratification slows billow growth while accelerating baroclinic shear production in the braid. Two-dimensional direct numerical simulations up to Reynolds numbers Re=10^7 quantify the role of viscosity. At high Re, we find that SSI indeed develops early in the braid, as predicted by the inviscid model, while the primary billow is still growing and before viscosity slows braid thinning. These results provide a mechanistic explanation for field observations of braid-dominated mixing and suggest that, at geophysically relevant Ri and Re, SSI can control the three-dimensional turbulent transition and ensuing diapycnal mixing by preceding and pre-empting both vortex pairing instabilities and secondary convective instabilities in the billow core.