A multi-scale model for the planetary and synoptic motions in the atmosphere

Abstract

A reduced asymptotic model valid for the planetary and synop tic scales in the atmo- 6 sphere is presented. The model is derived by applying a syste matic multiple scales asymp- 7 totic method to the full compressible flow equations in spher ical geometry. The synoptic 8 scale dynamics in the model is governed by modified quasi-geo strophic equations which take 9 into account planetary scale variations of the background s tratification and of the Corio- 10 lis parameter. The planetary scale background is described by the planetary geostrophic 11 equations and a new closure condition in the form of a two-sca le evolution equation for 12 the barotropic component of the background flow. This closur e equation provides a model 13 revealing an interaction mechanism from the synoptic scale to the planetary scale. 14 To obtain a quantitative assessment of the validity of the as ymptotics, the balances on 15 the planetary and synoptic scales are studied by utilizing a primitive equations model. For 16 that purpose spatial and temporal variations of different te rms in the vorticity equation are 17 analyzed. It is found that for planetary scale modes the hori zontal fluxes of relative and 18 planetary vorticity are nearly divergence free. It is shown that the results are consistent 19 with the asymptotic model.