On the vertical structure of wave forcing for the ocean circulation
Résumé
The conservation of momentum, when averaged over the phase of surface gravity waves can take two forms, whether or not the momentum variable contains the wave pseudo-momentum. The vertical profiles of the resulting wave-induced forces are discussed, with application to realistic condition. It was already proved that forces for the total momentum that use analytical functions of the local wave properties are necessarily inconsistent, and thus inaccurate at the lowest order. The consequences of these inaccuracies are explored here. In inviscid conditions, it is shown that large spurious currents of the order of 10 times the Strokes drift are generated on a sloping bottom, however small that slope is. These spurious velocities are reduced but are still significant when a strong vertical mixing is applied. In contrast, forces for the quasi-Eulerian mean momentum do not suffer from this inconsistency, and accurate numerical models can be developed. Choosing to solve for the quasi-Eulerian mean flow is also intrinsically more simple.
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