Multigrid Solution of Rotating, Stably Stratified Flows:

Abstract

Balance equation (BE) models describing accurate, gravity-wave-free states on the so-called “slow manifold” of the primitive equations are of wide and growing interest, both theoretical and practical, for geophysical fluid dynamics. Here, the three-dimensional BE are analyzed, and a multigrid algorithm with good convergence properties is developed and implemented in parallel on the shared-memory CRAY C-90 computer. It is the first solution method that is robust for large Rossby number near the limits of physical validity and mathematical well-posedness for the BE. An example is shown of a solution for decaying geostrophic turbulence with large Reynolds number. It exhibits a strong asymmetry in its coherent vortex dynamics: anti-cyclones on average become stronger and larger and proceed more rapidly in their merger and alignment interactions.