Energetics of low-order spectral systems

Abstract

The potential vorticity equation and the barotropic vorticity equation represented in spectral form in terms of solid spherical harmonics have been truncated to allow interaction between only one planetary wave and an arbitrary zonal flow. The analytic solutions in time which ensue from these truncated systems have been investigated in terms of the allowed nonlinear energy transfers. An energy flow diagram including potential and kinetic energy has been prepared and shows the direction and magnitude of exchange as it depends on the initial conditions. Maximum energy transfers and limitations of exchange amongst wave components are discussed. The linear solutions are considered and evaluated in terms of the exact solutions. Phase propagation and momentum transport in these systems are also investigated.