Coherent vortices and kinetic energy ribbons in asymptotic, quasi two-dimensional f-plane turbulence

This paper examines coherent vortices and spatial distributions of energy density in asymptotic states of numerically simulated, horizontally homogeneous, doubly periodic, quasi two-dimensional f-plane turbulence. With geophysical applications in mind, the paper progresses from freely decaying two-dimensional flow to freely decaying equivalent barotropic flow, freely decaying two-layer quasi-geostrophic (QG) flow, and, finally, statistically steady two-layer QG turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction. It is demonstrated here that, with suitable elaborations, a two-vortex state having a sinh-like potential vorticity/streamfunction $(q/ψ)$ scatter plot arises in all of these systems. This extends, at least qualitatively, previous work in inviscid and freely decaying two-dimensional flows to flows having stratification, forcing, and dissipation present simultaneously. Potential vorticity steps and ribbons of kinetic energy are shown to form in freely decaying equivalent barotropic flow and in the equivalent barotropic limit of baroclinically unstable flow, which occurs when Ekman damping is strong. Thus, contrary to expectations, strong friction can under some circumstances create rather than hinder the formation of sharp features. The ribbons are present, albeit less dramatically, in moderately damped baroclinically unstable turbulence, which is arguably a reasonable model for mid-ocean mesoscale eddies.