Induction and Transmission of Mean Zonal Flow by Quasi-geostrophic Disturbances

Abstract

The induction and transmission of mean motion by quasi-geostrophic disturbances are discussed. Two types of momentum transport process, i.e., that by a propagating internal wave packet and that by vortex tube stretching, are discussed by the use of a simple inviscid Boussinesq fluid channel model. The disturbance is excited by transient motion of the corrugated bottom, and the evolution of mean zonal flow is examined.
From a preliminary theoretical consideration, it is shown that the change of mean zonal momentum is caused by the divergence of wave momentum flux. Thus, the concept of ″momentum radiation born by a wave packet″ is useful in the problem of internal Rossby wave-mean zonal flow interaction. By applying the conservation law of wave action to the approximated zonal mean potential vorticity equation, a simple formula for the induced mean zonal flow is obtained. The utility of the formula is confirmed by the numerical computations and also by the application to the actual atmospheric situation.
Numerical time-integrations are conducted for three cases; (1) the Rossby parafeter β is zero, (2) β≠0 and the bottom moves westward and (3)β≠0 and the bottom moves eastward. In the first case, the induced mean zonal motion cannot be transmitted vertically deep into the fluid layer due to the stratification just as seen in the spin-up (or down) process of a stratified viscous fluid. In the second case, the mean zonal flow (easterly) is induced by a propagating internal Rossby wave packet and transmitted vertically upward accompanied with the wave packet.
In the third case, the westerly induction by vortex tube stretching process and the easterly acceleration by propagating internal waves counteract each other. Easterly flows are induced at upper levels and westerlies at lower levels.
As the applications of the present results, the effect of planetary waves on the earth's upper atmospheric mean circulation is discussed, and further some conjectures are made upon the solar atmospheric equatorial acceleration.