A SIMPLE FRICTION AND DIFFUSION SCHEME FOR PLANETARY GEOSTROPHIC BASIN MODELS

A simple friction and diffusion scheme is proposed for use with the ti me-dependent planetary geostrophic equations, which in their proper as ymptotic form cannot be solved in a closed basin. The resulting set of equations admits boundary conditions of no-normal flow and no-normal heat flux at all rigid boundaries, is amenable to efficient numerical solution, and may be solved with small heat (and salt) diffusivities. The scheme is formally. a minor modification of several others that ha ve recently been proposed but differs in significant details. Friction is represented by linear drag in the horizontal momentum equations, w hile the hydrostatic balance is retained exactly. The Laplacian vertic al and horizontal heat (and salt) diffusion are supplemented by biharm onic horizontal diffusion. The latter is necessary in order that the s moothness of the solution can be maintained up to and along the bounda ry, which is particularly important because the no-normal-flow conditi on is enforced as a differential equation that must be solved along th e boundary. The equations support a frictional western boundary curren t that is nearly adiabatic.