Recovery of atmospheric flow statistics in a general circulation model without nonlinear eddy-eddy interactions
The closure problem of turbulence arises because nonlinear interactions among turbulent fluctuations (eddies) lead to an infinite hierarchy of moment equations for flow statistics. Here we demonstrate with an idealized general circulation model (GCM) that many atmospheric flow statistics can already be recovered if the hierarchy of moment equations is truncated at second order, corresponding to the elimination of nonlinear eddy-eddy interactions. Some, but not all, features of the general circulation remain the same. The atmospheric eddy kinetic energy spectrum retains a −3 power-law range even though this is usually explained in terms of an enstrophy cascade mediated by nonlinear eddy-eddy interactions. Our results suggest that it may be possible to construct fast general circulation models that solve for atmospheric flow statistics directly rather than via simulation of individual eddies and their interactions.
© 2007 American Geophysical Union. Received 22 August 2007; revised 3 October 2007; accepted 12 October 2007; published 16 November 2007. This work was supported by the National Science Foundation (Grant ATM-0450059), the Davidow Discovery Fund, and a David and Lucile Packard Fellowship. The numerical simulations were performed on Caltech's Division of Geological and Planetary Sciences Dell cluster.
Published - pog_no_eddy_eddy.pdf