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The scaling argument developed by Larichev and Held (1995) for eddy amplitudesand fluxes in a horizontally homogeneous, two-layer model on an f-plane isextended to a beta-plane. In terms of the non-dimensional number x =U/(beta*lambda^2), where lambda is the deformation radius and U is the meanthermal wind, the result for the RMS eddy velocity V, the characteristicwavenumber of the energy-containing eddies and of the eddy-driven jets k, andthe magnitude of the eddy diffusivity for potential vorticity D, in the limitx>>1, are as follows: V/U ~ x ; k*lambda ~ 1/x ; D/(U*lambda) ~ x^2. Numericalsimulations provide qualitative support for this scaling, but suggest that itunderestimates the sensitivity of these eddy statistics to the value of x. Ageneralization that is applicable to continuous stratification is suggestedwhich leads to the estimates: V ~ 1/(beta T^2); k ~ beta*T; D ~1/{[beta^2][T^3]} where T is a time-scale determined by the environment; inparticular, it equals lambda/U in the two-layer model and N/(fS) in acontinuous flow with uniform shear S and stratification N. This same scalinghas also been suggested as relevant to a continuously stratified fluid in theopposite limit, x<<1 (Held, 1980). Therefore, we suggest that it may be ofgeneral relevance in planetary atmospheres and in the oceans.

A Scaling Theory for Horizontally Homogeneous, Baroclinically Unstable Flow on a Beta Plane