Breaking internal waves on sloping topography: connecting parcel displacements to overturn size and interior-boundary exchanges

Internal waves impinging on sloping topography can generate mixing through the formation of near-bottom bores and overturns in what has been called the ‘internal swash’ zone.Here we investigate the mixing generated during these breaking events, and the subsequent ventilation of the bottom boundary layer, across a realistic non-dimensional parameter space for the oceanusing three-dimensional large eddy simulations. Waves overturn and break at two points during awave period: when the downslope velocity is strongest and during the rapid onset of a dense, upslope bore. From the first overturning bore to the expulsion of fluid into the interior, there is a strong dependence on the length scale defined by the ratio of wave velocity over the background buoyancy frequency, an upper bound on the vertical parcel displacement an internal wave can cause. While this energetically-motivated vertical length scale is often seen in the context of lee wave generation over topography, the results discussed here suggest the same parameter can be used to determine the size of near-boundary overturns, the strength of the ensuing turbulent mixing, and the vertical scale of the along-isopycnal intrusions of fluid ejected from the boundary layer. Consideration of a volume budget of the near-boundary region highlights spatial and temporal variability that must be taken into account when determining the water-mass transformation during this process.