Vallis, Geoffrey K.
Physics of Fluids
We investigate the non-linear equilibration of a two-layer quasi-geostrophic ow in a channel with an initial eastward baroclinically unstable jet in the upper layer, paying particular attention to the role of bottom friction. In the limit of low bottom friction, classical theory of geostrophic turbulence predicts an inverse cascade of kinetic energy in the horizontal with condensation at the domain scale and barotropization in the vertical. By contrast, in the limit of large bottom friction, the ow is dominated by ribbons of high kinetic energy in the upper layer. These ribbons correspond to meandering jets separating regions of homogenized potential vorticity. We interpret these results by taking advantage of the peculiar conservation laws satis ed by this system: the dynamics can be recast in such a way that the initial eastward jet in the upper layer appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent ow that stirs this potential vorticity eld while conserving the global distribution of potential vorticity levels. Statistical mechanical theory of the 11/2 layer quasi-geostrophic model predicts the formation of two regions of homogenized potential vorticity separated by a minimal interface. We explain that cascade phenomenology leads to the same result. We then show that the dynamics of the ribbons results from a competition between a tendency to reach the equilibrium state and baroclinic instability that induces meanders of the interface. These meanders intermittently break and induce potential vorticity mixing, but the interface remains sharp throughout the ow evolution. We show that for some parameter regimes, the ribbons act as a mixing barrier which prevents relaxation toward equilibrium, favouring the emergence of multiple zonal (eastward) jets
Copyright (year) AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Phys. Fluids 26, 126605 (2014) and may be found at http://scitation.aip.org/content/aip/journal/pof2/26/12/10.1063/1.4904878
26, 126605 (2014)