The existence of two inertial ranges of forced homogeneous two-dimensional turbulence was conjectured about half a century ago. Given a forcing, confined to a typical wavenumber kf, a direct cascade with k^-3 scaling for kkf and an inverse cascade with k^-5/3 scaling for kkf would be established. Using a geometric integrator on a unit sphere we are able to provide robust evidence for the double cascade spectrum at modest numerical resolution.
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Cifani et al. (2022) studied this question.
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