Open Boundary Conditions for the Primitive and Boussinesq Equations

Abstract

It was shown by Oliger and Sundström, in 1978, that the initial boundary value problems for the hydrostatic primitive equations of meteorology and oceanography are ill posed if the boundaries are open and fixed in space. In this article it is shown, with theory and computation, that the same problems are well posed for a suitable set of local (pointwise applied) boundary conditions, if a mild vertical viscosity is added to the hydrostatic equation. Some indications on the behavior of the solutions, as the vertical viscosity parameter goes to zero, are also given. The Boussinesq equations are shown to be well posed in the same context of boundaries open and fixed in space. Finally, numerical simulations supporting the analysis are included.