Boundary Conditions for Limited-Area Forecasts

Abstract

The smoothness of solutions of the barotropic and baroclinic filtered and primitive equations in limited areas, subject to inflow boundary conditions, is in doubt due to the necessary occurrence of points on the boundaries where the flow is tangential. The problem is described in detail for the barotropic filtered equations; it is the classical situation of Cauchy data being specified for a hyperbolic equation on a boundary curve which is locally characteristic. A necessary set of conditions is developed for the data which must be satisfied if a smooth solution is to be ensured. The set is far too complex to allow their satisfaction in practice. Only the objectionable practice of introducing very high viscosity near the boundaries provides a simple way out of the problem. A more reasonable and not too complicated alternative is suggested.