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Pré-Publication, Document De Travail Année : 2010

On the vertical structure of adiabatic wave forcing for the ocean circulation. Part I: Theory and practical implementation

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. Various published equations give different vertical profiles of the resulting wave-induced forces, even in adiabatic conditions. The differences for the total momentum equations are due to different approximations of the wave-induced vertical flux of momentum. These differences are made explicit for all wave-averaged equations, using a generic form of the conservation equations. The effects of these approximations is revealed here, for cases with exact numerical solutions, using a coupled wave- current three-dimensional model based on WAVEWATCH III (Tolman 1998, 2009) and MARS3D (Lazure and Dumas 2008). The necessary modifications of the MARS3D flow model are detailed, and may be applied to any other primitive equation model. In realistic conditions, all published models for the total momentum that are based on local wave quantities yield spurious velocities over a sloping bottom. Without any viscosity, these currents are independent of the slope. These spurious velocities are reduced but are still significant when a realistic vertical mixing is applied. It is concluded that models for the total momentum based on local wave quantities are likely to have large errors for cross-shore fluxes outside of the surf zone. Such errors are found using the equations from Mellor (2003) or Mellor (2008b). In the latter case, the depth-integrated equations also appear inconsistent. For all such models, the errors can be traced to inconsistent approximations of the vertical flux wave momentum. In contrast, the quasi-Eulerian mean momentum does not suffer from this inconsistency, and accurate numerical models can be developed.
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Dates et versions

hal-00523388 , version 1 (05-10-2010)
hal-00523388 , version 2 (05-10-2010)
hal-00523388 , version 3 (14-09-2011)

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  • HAL Id : hal-00523388 , version 2

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Anne-Claire Bennis, Fabrice Ardhuin, Franck Dumas. On the vertical structure of adiabatic wave forcing for the ocean circulation. Part I: Theory and practical implementation. 2010. ⟨hal-00523388v2⟩
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