  From a scale analysis of hydrodynamic phenomena having a significant action
on the drift of an object in coastal ocean waters, we deduce equations modeling
the associated hydrodynamic fields over a time period of several weeks. These
models are essentially non linear hyperbolic systems of PDE involving a small
parameter. Then from the models we extract a simplified and nevertheless
typical one for which we prove that its classical solution exists on a time
interval which is independent of the small parameter. We then show that the
solution weak-* converges as the small parameter goes to zero and we
characterize the equation satisfied by the weak-* limit
