Particular exact solutions for a small area

Particular exact solutions of the hydrodynamic equations for a small sea are presented. They have been obtained under the following assumptions: sea on Earth's tangent plane; constant density; viscous-like stress tensor made up by an isotropic part and two other parts only horizontally isotropic; traceless and dissipative viscous-like stress tensor. In the search of particular exact solutions a supplementary hypothesis has been assumed: the advective part results from the gradient of suitable potentials (kinetic energy and rotational potential). Since the exact solution is considered as an initial solution in a perturbation approximation, the small Coriolis force has been neglected. For a small rectangular sea as the Adriatic sea, the solutions satisfy the conditions on the fixed boundaries (bottom and coastlines of the sea) with a very good approximation. The conditions at the free surface will be also discussed.