MULTIGRID SOLUTION OF ROTATING, STABLY STRATIFIED FLOWS - THE BALANCE-EQUATIONS AND THEIR TURBULENT DYNAMICS

Balance equation (BE) models describing accurate, gravity-wave-free st ales on the so-called ''slow manifold'' of the primitive equations are of wide and growing interest, both theoretical a nd practical, for ge ophysical fluid dynamics. Here, the three-dimensional BE are analyzed, and a multigrid algorithm with good convergence proper ties is develo ped and implemented in parallel on the shared-memory CRAY C-90 compute r. It is the first solution method that is robust for large Rossby num ber near the limits of physical validity and mathematical well-posedne ss for the BE. An example is shown of a solution for decaying geostrop hic turbulence with large Reynolds number. It exhibits a strong asymme try in its coherent vortex dynamics: anti-cyclones on average become s tronger and larger and proceed more rapidly in their merger and alignm ent interactions. (C) 1997 Academic Press.