Geostrophic Turbulence and Emergence of Eddies beyond the Radius of Deformation

Abstract

Geostrophic turbulence has traditionally been studied within the framework of the classical, quasi-geostrophic equation. This equation, valid only when vertical displacements are weak, possesses a symmetry between cyclonic and anticyclonic vortices that is not present in the primitive equations. Moreover, previous studies were restricted by length scales not in excess of the deformation radius. In an attempt to advance the study of unforced geostrophic turbulence, we address here the following questions: How is the energy cascade toward longer length scales affected beyond the deformation radius? And, what is the result of the cyclonic-anticyclonic asymmetry brought on by finite vertical displacements? Some answers are provided by numerical experiments using a generalized geostrophic equation. The energy cascade is found to come to a halt beyond the deformation radius. There, a statistical equilibrium is reached at a length scale prescribed as a combination of the deformation radius, the beta effect and the energy level of the system. Also, over the long run, one witnesses the emergence of few, large eddies, which all are anticyclonic and drift in a weaker, shorter-scale, quasi-geostrophic background. A simple theory capturing the essence of this bimodal distribution correctly predicts the bulk characteristics of the statistical equilibrium. Finally, some arguments are outlined to explain the selection of anticyclonic eddies and its relation to the statistical equilibrium.