Abstract

We present numerical and theoretical results on the energy cascade in a number of hydrodynamical systems. The systems that we study are the 2-D Navier-Stokes equations, the quasi-geostropophic equations, the so called primitive equations, in which hydrostatic balance is assumed and the Boussinesq equations. We find that the parameter which is regulating the strength of the downscale energy cascade is the Rossby number, with a decreasing amount of energy going into a downscale energy cascade with increasing rate of rotation. Stratification, on the other hand, does not inhibit a downscale energy cascade. Based on the primitive equations, we also present a new formulation of the spectral energy budged of the atmosphere, with spherical harmonics as base functions. Using this formulation we analyze data from two General Circulation Models. In one of the models we find evidence of a strong downscale energy cascade starting at 1000 km scales. In the other model, the cascade is inhibited by strongly dissipative processes at these scales