  Zonal flows are often found in rotating convective systems. Not only are
these jet-flows driven by the convection, they can also have a profound effect
on the nature of the convection. In this work the cylindrical annulus geometry
is exploited in order to perform nonlinear simulations seeking to produce
strong zonal flows and multiple jets. The parameter regime is extended to
Prandtl numbers that are not unity. Multiple jets are found to be spaced
according to a Rhines scaling based on the zonal flow speed, not the convective
velocity speed. Under certain conditions the nonlinear convection appears in
quasi-periodic bursts. A mean field stability analysis is performed around a
basic state containing both the zonal flow and the mean temperature gradient
found from the nonlinear simulations. The convective growth rates are found to
fluctuate with both of these mean quantities suggesting that both are necessary
in order for the bursting phenomenon to occur.
