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 language||English (US)|
|Number of pages||18|
|Journal||Journal of the Atmospheric Sciences|
|State||Published - Apr 1 1996|
All Science Journal Classification (ASJC) codes
- Atmospheric Science