[en] Two mathematical models for the study of mesoscale (tides, storm surges ...) and macroscale (general circulation ...) motions are described. Both models are derived from the GHER 3-D baroclinic turbulent closure primitive equation model and adapted to the specific spectral windows of, respectively, mesoscale and macroscale processes. Numerical methods are discussed: 3-D finite differences, mode-splitting, sigma-transform ... The mesoscale model is applied to the simulation of the M2 tide on the North-Western European Continental Shelf. The residual circulation model is based on time averaged primitive equations which explicitly include mesoscale Reynolds stresses that are computed by the mesoscale model. Preliminary results of the application of this model in typical summer conditions are presented.
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