4.10
Surface quasigeostrophic dynamics: eddy scales and tracer flux in forced-dissipative flow
C. Y. Tam, Princeton Univ., Princeton, NJ; and G. K. Vallis and K. S. Smith
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.
Session 4, Waves, Stability, and the General Circulation (Continued)
Tuesday, 5 June 2001, 1:30 PM-2:31 PM
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