The Role of Criticality on the Horizontal and Vertical Scales of Extratropical Eddies in a Dry GCM

This paper discusses the sensitivity of the horizontal and vertical scales of extratropical eddies when criticality is varied in a dry, primitive-equation, general circulation model. Criticality is a measure of extratropical isentropic slope and when defined appropriately its value is often close to 1 for Earth's climate. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and criticality is increased by increasing the thermal relaxation rate on the mean flow. When criticality varies near 1, it is shown that there exists a weakly nonlinear regime in which the eddy scale increases with criticality without involving an inverse cascade, while at the same time the Rossby radius may in fact decrease. The quasigeostrophic instability of the Charney problem is revisited. It is demonstrated that both the horizontal and vertical scales of the most unstable wave depend on criticality, and simple estimates for the two scales are obtained. The authors reconcile the opposite trends of the eddy scale and Rossby radius and obtain an estimate for the eddy scale in terms of the Rossby radius and criticality that is broadly consistent with simulations.