A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta plane

Isaac M. Held, Vitaly D. Larichev

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Abstract

The scaling argument developed by the authors in a previous work for eddy amplitudes and fluxes in a horizontally homogeneous, two-layer model on an f plane is extended to a β plane. In terms of the nondimensional number ξ = U/(βλ2), where λ is the deformation radius and U is the mean thermal wind, the result for the rms eddy velocity V, the characteristic wavenumber of the energy-containing eddies and of the eddy-driven jets kj, and the magnitude of the eddy diffusivity for potential vorticity D, in the limit ξ ≫ 1, are as follows: V/U ≈ξ, kiλ ≈ -1, D/(Uλ) ≈ ξ2. Numerical simulations provide qualitative support for this scaling but suggest that it underestimates the sensitivity of these eddy statistics to the value of ξ. A generalization that is applicable to continuous stratification is suggested that leads to the estimates V ≈ (βT2)-1, kj ≈ βT, D ≈ (β2T3) 1, where T is a timescale determined by the environment; in particular, it equals λU-1 in the two-layer model and N(f∂zU)-1 in a continuous flow with uniform shear and stratification. This same scaling has also been suggested as relevant to a continuously stratified fluid in the opposite limit, ξ ≪ 1. Therefore, the authors suggest that it may be of general relevance in planetary atmospheres and in the oceans.

Original languageEnglish (US)
Pages (from-to)946-963
Number of pages18
JournalJournal of the Atmospheric Sciences
Volume53
Issue number7
DOIs
StatePublished - Apr 1 1996

All Science Journal Classification (ASJC) codes

  • Atmospheric Science

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