Turbulent mixing in the oceanic boundary layer caused by internal wave reflection from sloping terrain

Abstract

Strong diapycnal mixing may occur in the benthic boundary layer caused by internal wave breakdown into turbulence near sloping boundaries. We report on numerical simulations of internal wave reflection and mixing in the bottom boundary layer over sloping topography. The experiments presented here are for critical angle wave reflection, defined as reflection from a bottom slope which matches the wave propagation angle. We demonstrate that transition of the wave field to stratified turbulence occurs for Reynolds number of approximately 1000. The turbulent boundary layer, of approximate thickness λ/3, where λ is the wavelength of the oncoming wave, exhibits quasi-periodic behavior, going through a cycle of energetic mixing and fine-scale development followed by a period of restratification and relaminarization. A distinctive thermal front develops in the boundary layer, which moves upslope at the phase speed of the oncoming wave. For steep slopes the flow resembles a turbulent bore, whereas for shallower slopes periodic mixing occurs across the breadth of the domain. The strongest period of mixing occurs during a phase when the oncoming wave sets up a strong downslope flow at the bottom boundary similar to the backwash on a beach. We find that diapycnal mixing extends into the interion stratified fluid and is not restricted to the turbulent boundary region. An important element of the communication of mixed fluid into the interior is the action of the internal wave field. It serves to continuously pump fresh stratified fluid into the mixed layer, while simultaneously extracting the mixed boundary fluid. The mixing efficiency of the wave breakdown process for these cases is found to be approximately 35%.