On the Excitation and Propagation of Zonal Winds in an Atmosphere with Newtonian Cooling

Abstract

A system of equations, including Newtonian cooling and valid away from the equator, is derived for atmospheric zonal winds and the associated zonal temperature and meridional circulation fields. A time scaling is introduced to distinguish three regimes of motion. For short time scales a variation of the usual nondissipative forced symmetric vortex problem is recovered. For intermediate time scales, a “diffusive model” is defined, while for long time scales a “steady state” model is defined. Two examples of the solution of the diffusive equation are given. From the first example we infer that our model is capable of explaining many of the observed features of the downward progression of the stratospheric biennial oscillation. Momentum is carried downward by Coriolis torques resulting from propagating meridional cells. The solutions of our second example describe transient zonal winds which resemble those observed to propagate downward from the stratopause in Meteorological Rocket Network data time-height sections. In general, dissipation relaxes the constraint of conservation of potential vorticity so that wave-like motions are possible when Newtonian cooling is present. The “steady state” model equation is solved by the method of Green's functions to obtain the forced temperature. For this model, there is a direct response to heating and only momentum fluxes force meridional circulations to give subsidence heating. It is found that the domain of influence of the temperature response to momentum fluxes lies below the source point. Our model suggests that observed long-period departures from radiative equilibrium in the atmosphere below the mesopause can be explained as due either to heating by horizontal eddy heat transports or to subsidence heating forced by eddy momentum fluxes.