Mixing near Boundaries

The presence of lateral boundaries fundamentally changes the circulation driven by turbulent mixing processes. In the open ocean, weak diapycnal mixing can drive strong horizontal recirculation gyres, such as is found in the classical Stommel / Arons abyssal circulation model. However, as this mixing is confined more closely to a lateral boundary, the potential vorticity balance changes such that the strong horizontal recirculations, which cross planetary vorticity contours, are replaced by weak unidirectional flow along potential vorticity contours into and out of the mixing region. If the horizontal scale of the mixing region drops below the relevant viscous length scale, the horizontal recirculation is essentially eliminated.

Lateral boundaries are similarly important for diapycnal mixing driven by atmospheric cooling. Essentially all of the downwelling limb of the thermohaline circulation takes place within narrow viscous boundary layers. For stratified flows, the downwelling occurs on horizontal scales of the internal deformation radius times the square root of the Prandl number. For weakly stratified flows, such as within the surface mixed layer, the downwelling is concentrated within very narrow boundary layers that scale as E^{1/3}, where E is a horizonal Ekman number (a Stewartson layer). For typical oceanographic parameters, these boundary layers are O(100 m) wide. While the details of the boundary layers depend on the degree of stratification, the common result is that the net vertical motions for buoyancy-forced downwelling of the thermohaline circulation occurs in narrow visous boundary layers. The near boundary regions are preferred because the lateral viscous flux of vorticity into the wall can balance the vertical stretching of planetary vorticity.

These results have strong implications for the impacts of near boundary processes (such as shelf-slope exchange, air-sea exchange, ice cover) on the large-scale thermohaline circulation. The dissipation experienced in such boundary layers can also alter the large-scale circulation around topographic features such as islands and ridges.