A CONTOUR-ADVECTIVE SEMI-LAGRANGIAN NUMERICAL ALGORITHM FOR SIMULATING FINE-SCALE CONSERVATIVE DYNAMICAL FIELDS

This paper describes a novel numerical algorithm for simulating the ev olution of fine-scale conservative fields in layer-wise two-dimensiona l flows, the most important examples of which are the earth's atmosphe re and oceans. The algorithm combines two radically different algorith ms, one Lagrangian and the other Eulerian, to achieve an unexpected ga in in computational efficiency. The algorithm is demonstrated for mult i-layer quasi-geostrophic flow, and results are presented for a simula tion of a tilted stratospheric polar vortex and of nearly-inviscid qua si-geostrophic turbulence. The turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-d imensional, vertically-coherent character of the flow. Ongoing extensi ons of the algorithm to the generally ageostrophic flows characteristi c of planetary fluid dynamics are outlined.