Transparent lateral boundary conditions for baroclinic waves II. Introducing potential vorticity waves

Transparent boundary conditions are derived for two systems of linear equations which support potential vorticity waves as well as barotropic and baroclinic waves. The first system, the one-dimensional shallow water equations, supports potential vorticity and barotropic waves only and it is used to lay the foundations for the second system, the two-dimensional linearized hydrostatic primitive equations, which supports multiple baroclinic and potential vorticity waves. For each system of equations the derived boundary conditions are shown to be stable and accurate for practical integrations despite the presence of dispersive waves.