VANISHING VISCOSITY IN THE BAROTROPIC BETA-PLANE

The initial boundary value problems associated with the inviscid barot ropic potential vorticity equation in the beta-plane and its viscous a nalogue 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, thi s convergence occurs as O(epsilon), where epsilon is the viscous param eter. This particular form of vanishing viscosity is of relevance in a nalysing viscosity induced advection for barotropic models. (C) 1997 A cademic Press.