### 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/(βλ^{2}), 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: V/U ≈ξ, k^{i}λ ≈ ^{-1}, D/(Uλ) ≈ ξ^{2}. 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 ≈ (βT^{2})^{-1}, k_{j} ≈ βT, D ≈ (β^{2}T^{3}) ^{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 atmospheres and in the oceans.

Original language | English (US) |
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Pages (from-to) | 946-963 |

Number of pages | 18 |

Journal | Journal of the Atmospheric Sciences |

Volume | 53 |

Issue number | 7 |

DOIs | |

State | Published - Apr 1 1996 |

### All Science Journal Classification (ASJC) codes

- Atmospheric Science