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Nonlocal energy transfers in generalized 2D turbulence

We study the spectral nonlocality of generalized energy transfers in alpha-turbulence models. These include several systems with geophysical relevance, including strongly rotating shallow-water quasi-geostrophic dynamics (alpha = -2), surface quasi-geostrophic dynamics (alpha = 1), familiar 2D flow (alpha = 2), and rotating shallow flow (alpha = 3), relevant to mantle dynamics. We first use Fjortoft-style arguments to study the dependence of wavevector triad geometry on alpha, then use a turbulence closure together with a similarity assumption to compute triad dynamical activity in first approximation. The closure allows us to calculate the contributions of variously-shaped triads to the generalized energy flux: as alpha increases, contributions from long, thin, nonlocal triads increasingly dominate. Interestingly, for alpha > 2.5, the net generalized energy flux is toward small scales (i.e. downscale), rather than large scales, which is counterintuitive: one generally expects net energy transfer to be toward large scales in 2D turbulence. The downscale flux may be due to the fact that very nonlocal triads, which play an increasingly important role as alpha increases, exchange most of their generalized energy with small scales.