Wave breaking due to internal wave-shear flow resonance over a sloping bottom

A new mechanism of internal wave breaking in the subsurface ocean layer is considered. The breaking is due to the 'resonant' interaction of shoaling l ong internal gravity waves with the subsurface shear current occurring in a resonance zone. Provided the wind-induced shear current is oriented onshor e, there exists a wide resonance zone, where internal wave celerity is clos e to the current velocity at the water surface and a particularly strong re sonant interaction of shoaling internal waves with the current takes place. A model to describe the coupled dynamics of the current perturbations trea ted as 'vorticity waves' and internal waves propagating over a sloping bott om is derived by asymptotic methods. The model generalizes the earlier one by Voronovich, Pelinovsky & Shrira (1998) by taking into account the mild b ottom slope typical of the oceanic shelf. The focus of the work is upon the effects on wave evolution due to the presence of the bottom slope. If the bottom is flat, the model admits a set of stationary solutions, both period ic and of solitary wave type, their amplitude being limited from above. The limiting waves are sharp crested. Space-time evolution of the waves propag ating over a sloping bottom is studied both by the adiabatic Whitham method for comparatively mild slopes and numerically for an arbitrary one. The pr incipal result is that all onshore propagating waves, however small their i nitial amplitudes are, inevitably reach the limiting amplitude within the r esonance zone and break. From the mathematical viewpoint the unique peculia rity of the problem lies in the fact that the wave evolution remains weakly nonlinear up to breaking. To address the situations when the subsurface cu rrent becomes strongly turbulent due to particularly intense wind-wave brea king, the effect of turbulent viscosity on the wave evolution is also inves tigated. The damping due to the turbulence results in a threshold in the in itial amplitudes of perturbations: the 'subcritical' perturbations are damp ed, the 'supercritical' ones inevitably break. As the breaking events occur mainly in the subsurface layer, they may contribute significantly to the m ixing and exchange processes at the air/sea interface and in creating signi ficant surface signatures.