Some Minimization Calculations Concerning the Effect of Horizontal Eddy Momentum Fluxes on the Equilibrium Zonal Mean Motions

Abstract

A simplified linearized two-level zonally averaged atmospheric model and the calculus of variations are used to address the following problems: Assuming fixed thermal forcing except for the longwave, radiative response to temperature, we find the equilibrium states of 1) minimum zonal kinetic energy (ZKE) and 2) minimum zonal kinetic plus zonal available potential energy (ZKE + ZAPE) for any distribution of horizontal eddy momentum fluxes. The solution to these problems contains interesting and suggestive features, among which are: The states of minimum ZKE or minimum ZKE + ZAPE contain a jet stream. The structure of the zonal winds is independent of the thermal forcing. The strength of the zonal winds is dependent on the thermal forcing. The horizontal eddy momentum fluxes that minimize the ZKE or ZKF + ZAPE can be up-gradient everywhere with respect to the upper level zonal mean zonal winds, down-gradient everywhere, or some combination, depending on the thermal forcing. ZKE minimization leads to a jet stream at 54° latitude independent of any external parameters. Minimization of ZKE + ZAPE loads to a jet stream at 35° for a planet of the earth's radius and static stability parameter when the top of the model is at approximately 300 mb.