Ribbon Turbulence

TL;DR

This paper explores how bottom friction influences the non-linear behavior of two-layer quasi-geostrophic flows, revealing a transition from inverse energy cascade to ribbon-dominated jets and barriers to mixing.

Contribution

It demonstrates how bottom friction alters flow structures, showing the emergence of ribbons and jets, and applies statistical mechanics to explain potential vorticity dynamics.

Findings

Low bottom friction leads to inverse cascade and barotropization.

High bottom friction results in ribbon-like jets and potential vorticity barriers.

Ribbons can prevent flow relaxation and promote multiple jets.

Abstract

We investigate the non-linear equilibration of a two-layer quasi-geostrophic flow in a channel forced by an imposed unstable zonal mean flow, 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 on the vertical. By contrast, in the limit of large bottom friction, the flow 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 result by taking advantage of the peculiar conservation laws satisfied by this system: the dynamics can be recast in such a way that the imposed mean flow appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent flow that stirs this potential vorticity field while conserving the global distribution of potential vorticity levels. Statistical mechanical theory of the 1-1/2 layer quasi-geostrophic model predict the formation of two regions of homogenized potential vorticity separated by a minimal interface. We show that the dynamics of the ribbons results from a competition between a tendency to reach this 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 flow evolution. We show that for some parameter regimes, the ribbons act as a mixing barrier which prevent relaxation toward equilibrium, favouring the emergence of multiple zonal jets.