Vanishing viscosity in the barotropic beta-plane

The initial boundary value problems associated with the inviscid barotropic potential vorticity equation in the beta-plane and its viscous analogue are considered. It is shown that the solution velocity to the viscous equation converges to the inviscid solution in a C-1 sense for finite times and that, under additional smoothness assumptions on the inviscid flow, this convergence can be extended to C-3. Moreover, this convergence occurs as O(epsilon), where epsilon is the viscous parameter. This particular form of vanishing viscosity is of relevance in analysing viscosity induced advection for barotropic models. (C) 1997 Academic Press.