Dg. Dritschel et Mhp. Ambaum, A CONTOUR-ADVECTIVE SEMI-LAGRANGIAN NUMERICAL ALGORITHM FOR SIMULATING FINE-SCALE CONSERVATIVE DYNAMICAL FIELDS, Quarterly Journal of the Royal Meteorological Society, 123(540), 1997, pp. 1097-1130
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.