The free surface of a coupled ocean–atmosphere model due to forcing effects

In this work, we consider external effects on a coupled shallow water ocean–atmosphere model. The forced shallow water equation due to the wind action is studied through a decomposition technique. Induced free perturbations of the permanent response are identified by using a spectral operator basis that is generated by a dynamical Green function. This later was determined through a spectral technique. By using the semi-lagrangian method, we compute the non-linear response of the full model due to a shear stress that comes from the action of the wind at the ocean surface.