  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.
