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.

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