Atmospheric Energy Cycle Viewed from Wave–Mean-Flow Interaction and Lagrangian Mean Circulation

Abstract

A formulation is proposed to analyze energetics of the global atmosphere. To see effects of wave?mean-flow interaction and Lagrangian mean meridional circulation from nonlinear and nongeostrophic senses, rate equations of potential and kinetic energies are derived from primitive equations expressed in terms of the pressure?isentrope hybrid?vertical coordinates. The present scheme does not directly exchange the zonal mean available potential energy with the eddy available potential energy but does exchange the zonal mean kinetic energy with the eddy available potential energy. The latter is contributed to by the vertical divergence of the form drag over isentropic surfaces, which is the major term of the Eliassen?Palm flux divergence. One application is made to two-dimensional (a longitude?altitude plane) channel fluid. This system has no energy conversion between the mean and eddy kinetic energies. In the process of wave?mean-flow interactions, the mean flow amplifies waves through the advection of positive isentropic thickness anomaly toward higher portions over undulated isentropes and, accordingly, the mean kinetic energy is converted into the eddy available potential energy. The eddy available potential energy is converted into the eddy kinetic energy when the flow field deforms, conserving the mean zonal flows. Another application is made to baroclinic instability waves. The zonal mean available potential energy is released to the zonal mean kinetic energy by driving mean meridional wind. Simultaneously the kinetic energy of mean zonal wind is converted into the eddy available potential energy through wave?mean-flow interactions. Under the geostrophic equilibrium condition, these two conversions are almost equal to each other. Geostrophic adjustments may assist conversions from the eddy available potential energy into the eddy kinetic energy. All the processes might be the main stream of dynamical energy flows at mid- and high latitudes.