Vanishing Viscosity in the Barotropic b-Plane

The initial boundary value problems associated with the inviscid barotropic potential vorticity equation in the b-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 C1 sense for finite times and that, under additional smoothness assumptions on the inviscid flow, this convergence can be extended to C3. Moreover, this convergence occurs as O « ., where « is the viscous parameter. This particular form of vanishing viscosity is of relevance in analysing viscosity induced advection for barotropic models