A General Three-Dimensional Transformed Eulerian Mean Formulation

Abstract

The transformed Eulerian mean (TEM) formulation for equations of motion, which was originally defined for waves on a zonally averaged flow, is extended three-dimensionally to a non-hydrostatic Boussinesq fluid in the general coordinate system. The three-dimensional antisymmetric diffusion tensor that plays a central role in defining the residual circulation and the Eliassen-Palm flux tensor is derived systematically by assuming that eddies consist of neutral waves. A modification of the formulation for application to practical data analyses is made by introducing a symmetric eddy diffusion tensor.