On resolution in atmospheric numerical models and cascade processes

Abstract

The implications of cascade processes in barotropic and quasi-geostrophic models are reviewed using conservation of kinetic energy and enstrophy in the barotropic case and conservation of the sum of available potential and kinetic energy and of potential, quasi-geostrophic enstrophy in the baroclinic case. The upper limit for energy cascades across a given spherical wave number, obtained from Fj0rtofts theorem, is in the barotropic case used to estimate the resolution necessary to prevent almost all cascades across the maximum wave number in the computational spectrum. The generalization to quasi-geostrophic, baroclinic models gives the possibility to estimate the horizontal and vertical resolutions required to limit the cascade of total energy across the maximum three-dimensional, spherical wave number in the computational resolution to a small fraction of the initial total energy.