Instability and Mixing of Stratified Shear Layers Forced by Internal Wave Strain

Turbulence generated by breaking internal waves is an important source of mixing in the ocean interior. This is often interpreted in terms of vertical shear and associated shear instabilities; however, observations suggest that the vertical strain caused by internal waves may also impact the stability and subsequent mixing of the flows through which they propagate (e.g.~Alford and Pinkel, JPO, 2000). Here, we idealize this process by imposing a background wave which is spatially and temporally periodic onto a stably-stratified shear flow. We examine the stability of this complicated, time-dependent base flow over a range of parameters in order to identify and quantify the effect of the internal wave strain on the overall flow stability. Using a direct-adjoint looping method, we find the most unstable linear perturbations over a finite time interval. Direct numerical simulations are then used to examine the nonlinear evolution and subsequent mixing. These results could be useful when developing parameterizations of ocean mixing which include the effects of vertical strain.