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- Author or Editor: Vitaly D. Larichev x
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Isaac M. Held
and
Vitaly D. Larichev
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 k
j
, and the magnitude of the eddy diffusivity for potential vorticity D, in the limit ξ ≫ 1, are as follows:
VUkj
−1DU2
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
VT2−1kj
TD2T3−1
where T is a timescale determined by the environment; in particular, it equals λU
−1 in the two-layer model and N(f∂
z
U)−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 atmosphere and in the oceans.
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 k
j
, and the magnitude of the eddy diffusivity for potential vorticity D, in the limit ξ ≫ 1, are as follows:
VUkj
−1DU2
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
VT2−1kj
TD2T3−1
where T is a timescale determined by the environment; in particular, it equals λU
−1 in the two-layer model and N(f∂
z
U)−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 atmosphere and in the oceans.
