Pathways to turbulence from internal waves in stratified horizontal shear flows*

We use direct numerical simulations to study the behaviour of a monochromatic internal wave packet incident on a horizontal shear layer in a uniform vertical density stratification. The interaction of the wave and shear flow is controlled primarily by two fundamental limiting mechanisms, namely the advection of momentum across the shear layer by the wave and the Doppler shifting of the wave frequency by the shear. When Doppler shifting is weak, wave advection of momentum creates enhanced local vertical shear. On the other hand, when Doppler shifting is strong, the wave becomes trapped within the shear layer when its intrinsic frequency becomes equal to the buoyancy frequency and may overturn convectively. By varying the relative importance of stratification and horizontal shear (the Froude number) and the dimensionless wave vector k, we demonstrate that the properties of the turbulence produced by wave breaking depend sensitively on the the relative importance of the two mechanisms outlined above. There are significant implications for the parameterization of stratified turbulent mixing and dissipation in oceanographic flows.