Title:

Instabilities of a shear layer in a barotropic rotating fluid

Above a critical value of horizontal stress, the flow within a bounded system
in rotation is driven to an unstable limit, beyond which it develops chains of
vortices. The number of these vortices depends not only upon the value of the
stress imposed but also on the sense of the shear in some configurations, highlighting
discrepancies between earlier experiments. Quasigeostrophic theory,
however, predicts that there should be no qualitative differences with respect
to the sign of the forcing.
We have studied barotropic instability in laboratory experiments with flat
cylindrical geometry, where a detached shear layer occurs tangent to differentially
rotating sections. These sections can either be two discs placed at the
top and bottom of the tank or a single thick disc immersed in the fluid. \Vhen
a single thick disc is used, we observe that the azimuthal wavenumber depends
on the sign of differential rotation.
\Vith axisymmetric numerical simulations, we were able to study the differences
in the meridional circulation for different configurations and sign of
forcing. \Vhen two discs are used, the circulation occurs in pairs of counterrotating
cells of similar size, if the forcing is weak. For strong and positive
forcing only, centrifugal instability sets in. \Vhen a single disc is used, one of
the circulation cells is typically much stronger than the other and the flow is
strongly asymmetric in radius.
The influence of a topographic ,aeffect was also investigated in laboratory
experiments, using four distinct sloping bottom combinations with the setup of
the two discs. In the configurations studied, unstable modes of shear instability
can be stabilised by topography, depending on the combination of sgn(,B) and
sign of forcing.
Finally, we studied a possible example of barotropic instability in planetary
atmospheres and propose that longlived polygonal jets such as Saturn's north
polar hexagon should be interpreted as a finiteamplitude, nonlinear equilibration
of a barotropic instability of Saturn's zonal jet.
