This research was supported by the EU FP-7 under the PIRG03-GA-2008-230958 Marie Curie Grant. The authors acknowledge the hospitality of the Aspen Center for Physics supported by the NSF (under Grant 1066293), where part of this work was written. The authors would also like to thank Kaushik Srinivasan and Bill Young for fruitful discussions and an early version of their manuscript and Brian Farrell and Freddy Bouchet for stimulating discussions on the results of this work.
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In Earth's atmosphere, the size of the eddies and the jet are about 103 km and 4 × 103 km, respectively, and the eddy dissipation time scale is about 2 days, so that
Similar results are also obtained in the opposite limit of a meridionally confined forcing (kfδ ≪ 1). The only exception is the limiting case of an uncorrelated forcing (δ → 0), for which the only nonzero coefficient is AP leading to downgradient hyperdiffusive fluxes (cf. appendix B).
Note that the angles θm = ±π/6 correspond to the orientations at which a wave with initial vorticity B(k) maximizes the momentum flux amplitude. If the wave were introduced with initial energy E(k), then the momentum fluxes of the carrier wave ignoring dissipation would be given by
To investigate the third term, we need to take into account the third derivative of δU in (36). However, since this turns out to be a stabilizing term for the cases considered, we will not pursue this further.
The limit βLf/r < 1 ensures that the first terms in the denominator are at least order