On the mountain torque in barotropic planetary flow

Abstract

AbstractAn attempt is made to understand the long‐term balance of the total relative angular momentum M of an inviscid barotropic fluid forced by orography. the problem is treated by integrating the barotropic potential vorticity equation with the β‐plane approximation, and on the sphere, using spectral methods. First, a highly truncated system containing only the superrotational flow and one wave component is studied by analytical means. A fairly complete understanding of the behaviour and the climatic mean value of M is achieved. Then, less truncated systems with up to five zonal wave‐numbers are investigated by numerical integrations. It turns out that a climatic mean value can be ascribed to M if the integration is carried out for several weeks or more. It is demonstrated that this long‐term mean value can be estimated reasonably weil on the basis of the study of the highly truncated system. A possible application of these results to more realistic fluid systems is suggested.