A new mechanism of internal wave breaking in the subsurface ocean layer is considered.
The breaking is due to the ‘resonant’ interaction of shoaling long internal gravity
waves with the subsurface shear current occurring in a resonance zone. Provided the
wind-induced shear current is oriented onshore, there exists a wide resonance zone,
where internal wave celerity is close to the current velocity at the water surface and
a particularly strong resonant interaction of shoaling internal waves with the current
takes place. A model to describe the coupled dynamics of the current perturbations
treated as ‘vorticity waves’ and internal waves propagating over a sloping bottom is
derived by asymptotic methods. The model generalizes the earlier one by Voronovich,
Pelinovsky & Shrira (1998) by taking into account the mild bottom 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 periodic and of solitary wave type, their amplitude being
limited from above. The limiting waves are sharp crested. Space–time evolution of the
waves propagating over a sloping bottom is studied both by the adiabatic Whitham
method for comparatively mild slopes and numerically for an arbitrary one. The
principal result is that all onshore propagating waves, however small their initial
amplitudes are, inevitably reach the limiting amplitude within the resonance zone
and break. From the mathematical viewpoint the unique peculiarity of the problem
lies in the fact that the wave evolution remains weakly nonlinear up to breaking. To
address the situations when the subsurface current becomes strongly turbulent due
to particularly intense wind-wave breaking, the effect of turbulent viscosity on the
wave evolution is also investigated. The damping due to the turbulence results in a
threshold in the initial amplitudes of perturbations: the ‘subcritical’ perturbations are
damped, the ‘supercritical’ ones inevitably break. As the breaking events occur mainly
in the subsurface layer, they may contribute significantly to the mixing and exchange
processes at the air/sea interface and in creating significant surface signatures.