Transcritical generation of nonlinear internal waves in the presence of background shear flow

Abstract

While the occurrence of large amplitude internal waves in the Earth's natural bodies of water is widely documented, the generation of these waves remains an active area of exploration. We discuss numerical simulations of transcritical flows of a density stratified fluid with a dual focus on the role of a background shear current and transitions of the background current from super to subcritical. We demonstrate that the presence of a background shear can lead to the formation of large quasi-trapped regions of high vorticity over the downstream slope of the topography, but that this vorticity leads to only moderate perturbations of the underlying pycnocline, and hence that a wave and instability can co-exist for long times. Subsequently, we demonstrate the existence of hysteresis in the wave amplitude when the current is accelerated to supercritical then decelerated to subcritical, as opposed to accelerated to the subcritical value from rest. Finally, we explore situations in which the background shear is strong enough to preclude the formation of solitary-like waves, and discuss possible implications for the coastal ocean.