Diminishing inverse transfer and non-cascading dynamics in surface quasi-geostrophic turbulence

he inverse transfer in the forced-dissipative surface quasi-geostrophic equation is studied, when the natural dissipation operator mu(-Delta)(1/2) lis employed. The nonlinear transfer of this system conserves the two quadratic quantities psi(1) = (vertical bar(-Delta)(1/4) psi vertical bar(2)>/2 and psi(2) = (vertical bar(-Delta)(1/2) psi vertical bar(2))/2 (kinetic energy), where psi is the stream function and <.> denotes a spatial average. In the limit of infinite domain, the kinetic energy density psi(2) remains bounded, for the natural dissipation operator. For the power-law inverse-transfer region, the inverse flux of T-1 diminishes as it proceeds toward sufficiently low wavenumbers, whenever the kinetic energy psi(2) remains bounded. This implies that no persistent (non-dissipative) inverse cascade of psi(1) to ever-lower wavenumbers is sustainable, as long as the dissipation parameter mu it is held fixed. This result does not rule out the possibility that for sufficiently small mu, a finite inverse flux would reach a certain low wavenumber. Numerical results supporting the theoretical predictions are presented. (c) 2005 Elsevier B.V. All rights reserved.