Internal wave breaking

Internal wave breaking is a process during which internal gravity waves attain a large amplitude compared to their length scale, become nonlinearly unstable and finally break. This process is accompanied by turbulent dissipation and mixing. As internal gravity waves carry energy and momentum from the environment of their inception, breaking and subsequent turbulent mixing affects the fluid characteristics in locations of breaking. Consequently, internal wave breaking influences even the large scale flows and composition in both the ocean and the atmosphere. In the atmosphere, momentum deposition by internal wave breaking plays a key role in atmospheric phenomena such as the Quasi-Biennial Oscillation and the Brewer-Dobson Circulation. In the deep ocean, mixing induced by internal wave breaking is an important driver of the meridional overturning circulation. On smaller scales, breaking-induced mixing is important for sediment transport and for nutrient supply to the photic zone. Most breaking of oceanic internal waves occurs in continental shelves, well below the ocean surface, which makes it a difficult phenomenon to observe. The contribution of breaking internal waves to many atmospheric and ocean processes makes it important to parametrize their effects in weather and climate models.

Breaking mechanisms Similar to what happens to surface gravity waves near a coastline, when internal waves enter shallow waters and encounter steep topography, they steepen and grow in amplitude in a nonlinear process known as shoaling. As the wave travels over topography with increasing height, bed friction leads to internal waves becoming asymmetrical with an increasing steepness. These nonlinear internal waves on a shallow slope are generally referred to as internal bores. Wave height and energy increase until a critical steepness is reached, whereafter the wave breaks by convective, Kelvin-Helmholtz or parametric subharmonic instability. Due to the relatively small density differences (and thus small restoring forces) over the ocean depth, ocean internal waves may reach amplitudes up to around 100 m. Analogous to surface wave breaking in the region known as the surf zone, internal breaking waves dissipate energy in what is known as the internal surf zone.

Internal tide breaking Internal tidal waves are internal waves at tidal frequency in the ocean, which are generated by the interaction of the tide with the ocean topography. Alongside internal inertial waves, they constitute the majority of the ocean internal wavefield. The internal tides consist of so-called low modes and high modes with varying vertical wavelengths. As these waves propagate, the high modes tend to dissipate their energy quickly, leading to the low modes to dominate further away from the location of their generation. Low mode internal waves, with wavelengths exceeding 100 km, generated by either tides or winds acting on the sea surface, can travel thousands of kilometers from their regions of generation, where they will eventually encounter sloping topography and break. When this happens, isopycnals become steeper and steeper, where the wavefront is followed by a sharp temperature drop. This then leads to an unstable density profile that eventually overturns and breaks. The magnitude of the topographic slope and the slope of the internal wave beam dictate where internal waves break. The slope of an internal wave beam ( r {\displaystyle r} ) can be expressed as the ratio between its horizontal ( k {\displaystyle k} ) and vertical ( m {\displaystyle m} ) wavenumbers:

r = | k m | = ω 2 − f 2 N 2 − ω 2 {\displaystyle r={\Bigg |}{\frac {k}{m}}{\Bigg |}={\sqrt {\frac {\omega ^{2}-f^{2}}{N^{2}-\omega ^{2}}}}}

where N {\displaystyle N} is the buoyancy frequency (or Brunt-Väisälä frequency), f {\displaystyle f} is the Coriolis frequency and ω {\displaystyle \omega } is the wave frequency in the dispersion relation that governs the propagation of internal waves in a continuously stratified and rotating medium:

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