Theory of Planetary Wave-Zonal Flow Interaction

Abstract

Small amplitude planetary waves are superimposed on a mean zonal flow with arbitrary horizontal and vertical shears. An expression is derived for the change of the zonal wind and temperature field forced by statistically stationary eddies satisfying a source-free planetary wave equation. This result depends on the existence of singular lines, where the phase speed of an elementary wave is equal to the mean zonal wind speed, or on the presence of a Newtonian cooling process. Second-order interactions vanish when both of these phenomena are absent. The planetary wave-zonal flow interaction is discussed in terms of the eddy transport of potential vorticity. The theory provides a partial interpretation of the maintenance of atmospheric zonal flows, such as that of the wintertime stratosphere, by planetary waves propagating from some other region of the atmosphere.