We study two-dimensional incompressible turbulence on the beta plane and propose a modification to the Rhines scale that takes into account the bottom friction. The modified Rhines scale is studied numerically, and found to predict accurately the jet number and the energy peak of the beta-plane turbulence for strong beta. The intermediate cases show a transition from the (isotropic) friction scale to the Rhines one, as the proper halting scale for the inverse cascade.
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Danilov et al. (2002) studied this question.
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