Generation of zonal flows by Rossby waves

It is shown that large scale zonal flows in a rotating fluid can be excited due to the Reynolds stresses of short scale Rossby waves. By employing the equations for a shallow rotating fluid in the geostrophic approximation, we obtain a Charney equation for nonlinearly coupled Rossby waves and zonal flows. The equation is then decomposed into two equations; one for short scale (comparable to the Rossby radius) Rossby waves in the presence of zonal flows, and another for zonal flows which are driven by the Reynolds stresses of the Rossby waves. Our pair of equations is then Fourier transformed to obtain a nonlinear dispersion relation, which admits the excitation of zonal flows due to the Rossby pumping energy. The present investigation thus provides a nonlinear mechanism for the energy transfer from short scale Rossby waves to large scale zonal flows. (C) 2002 Elsevier Science B.V All rights reserved.