On atmospheric energy cascades

Abstract

The advection terms in the atmospheric equations of motion will in the spectral domain result in an exchange of available potential and kinetic energies between the various wave numbers. Observational studies have demonstrated that while the available potential energy cascades from lower to higher wave numbers, the kinetic energy is cascaded from the middle wave numbers to both the high and the low wave numbers supposedly due to the fact that the energy conversion from available potential energy to kinetic energy is large in an interval of the wave number scale. The purpose of the present paper is to reproduce some major aspects of these energy cascade processes using first an extremely simple model based on a homogeneous fluid with a free surface. The driving factor in the model is the use of adding and subtracting fluid in such a way that the net addition vanishes. The model will furthermore be restricted to one space dimension in the west-east direction retaining the nonlinearities in the advection terms. The model equations, containing forcing and dissipation, are integrated numerically to a steady state. Evaluations of the energy generation, conversions and dissipations show that the model cascade processes behave correctly with respect to direction and magnitude as compared to the other energy conversions in the model and qualitatively correct compared to observational studies. The second model is based on the primitive equations for the two horizontal wind components and the thermodynamic equation including a specified heating which is independent of time. This model is also treated in the zonal direction only and in wave number space. The model gives good simulations of the transfer of both available potential and kinetic energy as functions of the wave number.