On the spectral changes of energy in the equivalent barotropic model

Abstract

Using the beta-plane approximation, a pair of conservation requirements are derived for the equivalent barotropic model. These conservation requirements provide very helpful informations about spectral solutions of the equivalent barotropic model. Basing on these conservation requirements, the changes in time of the spectral distribution of energy is discussed. It is found that only two components cannot exchange energy between themselves. For the possible exchange of energy, at least, three components are required. A condition is derived for the transfer of total energy to the scales less than or equal to a given one. Also, the upper limit to the flow of energy to the scales less than or equal to a given one is found. Again, the application of the results to the spectral instability is discussed.