Abstract

We study the spectral nonlocality of generalized energy transfers in alpha-turbulence models. These include planetary geostrophic dynamics (alpha = -2), surface quasi-geostrophic dynamics (alpha = 1), familiar 2D Navier-Stokes flow (alpha = 2), and rotating shallow flow (RSF, alpha = 3), the isotropic limit of a mantle convection model. We first use Fjortoft-style arguments to study the dependence of wavevector triad geometry on alpha. Such arguments provide no information on triad activity. We then derive for alpha-turbulence the eddy damped quasinormal Markovian (EDQNM) closure. Combined with a similarity assumption, this allows us to calculate, in first approximation, the contributions of particular triad shapes to the generalized energy flux. As alpha increases, contributions from long, thin, nonlocal triads increasingly dominate the flux; starting at alpha = 4, the flux diverges, signaling complete breakdown of transfer locality. In comparison, the EDQNM generalized enstrophy flux diverges at alpha = 2.

Interestingly, for alpha > 2.5, the net generalized energy flux associated with the self-similar inertial range solution is toward small scales (i.e. downscale), rather than large scales. This downscale flux reflects the relationship between the similarity spectrum and the two-temperature equipartition spectrum calculated for a spectrally truncated fluid.