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 nonhydrostatic 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. © 2010, the Meteorological Society of Japan.