Surface quasigeostrophic dynamics: eddy scales and tracer flux in forced-dissipative flow

We investigate turbulent flow in the Surface Quasigeostrophic (SQG) system, which arises from stratified quasigeostrophic dynamics as the two-dimensional prognostic equation for (upper or lower) surface temperature, in the limit of constant interior potential vorticity. Fully developed turbulence in SQG is similar to its counterpart in two-dimensional flow; Kolmogorov-Kraichnan type scaling theory can be readily applied. Such turbulence is simulated with a spectral model using 512^2 degrees of freedom, stirred by high wavenumber random forcing. A sub-inertial range exists, with an energy spectrum which agrees well with theoretical prediction. A Kolmogorov constant of about 9 is found. The upscale cascade of available potential energy is halted and dissipated by linear drag; the scale at which the cascade terminates is inversely proportional to the drag itself, in accordance with a simple scaling argument. Moreover, a universal spectrum is derived which predicts the non-dimensional proportionality constant for the stopping scale in terms of the relevant Kolmogorov constant. Finally, we predict the spectra and flux of a passive tracer, forced by a large-scale mean gradient and advected along with the flow. The tracer dynamics are also tested numerically, and the resulting statistics are found to be consistent with the predictions.