Meta-stability of equilibrium statistical structures for prototype geophysical flows with damping and driving

The most-probable states of an equilibrium statistical theory, which consis t of monopole vortices, dipole vortex streets, and zonal shear flows for va rious parameter regimes, are shown to be meta-stable with respect to damped and driven quasigeostrophic dynamics in a periodic beta -plane channel. Th rough a series of numerical experiments that include (1) pure decay, (2) bo th damping and driving, and (3) both direct and inverse cascades of energy, we demonstrate that statistically most-probable states evolve into other m ost-probable states with high accuracy, even as the energy changes substant ially and the flow undergoes topological transitions from vortex to shear B ow, or vice versa. The predictions of the equilibrium statistical theory ar e calculated by an algorithm, which we call an "approximate dynamics", that constructs the most-probable states from the instantaneous values of a few quantities in the evolving flow. Qualitatively, the approximate dynamics p redicts the correct topological structure - whether vortex flow or zonal sh eer - in the evolving Row. Quantitatively, the predictions are evaluated by measuring the relative errors between the velocity fields and vorticity fi elds of the evolving flow and the most-probable states. For evolving monopo le vortices we find that errors in the velocity field are generally near 5% and errors in the potential vorticity field are generally near 15%. For ev olving dipole vortex streets, the magnitude of the relative errors depends on the amplitude of the localized forcing. For pure decay, the errors in th e velocity held are generally near 5% and errors in the vorticity field are generally near 12%; for runs in which the Bow is strongly forced by small- scale vortices whose amplitude is nearly 3/10 the peak vorticity in the ini tial flow, the errors in the velocity field can rise to 20% and the errors in the vorticity field rise to 40%. (C) 2001 Elsevier Science B.V. All righ ts reserved.