Premium
Finite amplitude, steady Rossby waves and mean flows: Analytical illustrations of the Charney‐Drazin non‐acceleration theorem
Author(s) -
White A. A.
Publication year - 1986
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49711247311
Subject(s) - baroclinity , barotropic fluid , rossby wave , potential vorticity , vorticity , rossby radius of deformation , zonal flow (plasma) , mechanics , physics , rossby number , mean flow , steady state (chemistry) , classical mechanics , turbulence , vortex , atmospheric sciences , plasma , quantum mechanics , tokamak , chemistry
Exact steady‐state solutions of the nonlinear quasi‐geostrophic equations are used to illustrate some important repercussions of the Charney—Drazin theorem on the non‐acceleration of zonal mean flows by steady conservative waves. The solutions, which are similar to those discussed by Kuo in 1959, consist of spatially non‐uniform zonal flows and barotropic and baroclinic Rossby waves each having the same three‐dimensional wavenumber; a uniform zonal flow is also allowed. Two examples, both consisting of an internal jet zonal flow, a barotropic Rossby wave and a baroclinic Rossby wave, are considered. The absence of wave/mean interaction in these steady‐state solutions is clearly reflected in the absence of poleward eddy potential vorticity fluxes, but is disguised by the existence of non‐zero poleward eddy heat and zonal momentum fluxes and active Lorenz energy cycles. The solutions thus exhibit the same behaviour as the linearized examples discussed previously by various workers, and emphasize the danger of inferring from incomplete vorticity, energy or heat budget analyses that wave forcing (or maintenance) of Eulerian mean flows by eddy motion is taking place. One of the solutions (which is valid in a laterally open domain) is examined as a possible theoretical model of the steady waves seen in rotating annulus experiments. The spatial variations of the zonal mean flow and the eddy heat and momentum fluxes are in reasonable agreement with the results of a numerical simulation of a steady annulus wave, but the analytical solution is unsatisfactory in some other respects. It is clear that dissipative effects must be represented in any complete theoretical model of these steady waves.