Jupiter and Saturn have long-lived east-west (zonal) flows. Little is known about what sets their velocity scales or their length scales (i.e., the number of zones on each planet). Typically, when coherent features spontaneously form in turbulent flows they span a range of scales. In the rare cases that the features all have the same size, their lengths are usually determined directly by the boundary or forcing length scales: the scale of granulation on the Sun (due to turbulent convection cells) is set by the depth of the convective zone; the diameters of turbulent Taylor vortices in a Couette apparatus are determined by the width of the apparatus; Jupiter's long-lived vortices, such as the Red Spot, are set by the widths of the local zonal flows in which they are situated. By examining a simple forced/dissipated flow we show that the widths of zonal flows on a --plane are determined by a subtle combination of the forcing and dissipation and not set by boundary conditions or by the length scale of the forcing. We show that under a wide variety of conditions a turbulent flow without east-west winds forms via a reverse energy cascade. Under some circumstances zonal flows all with approximately the same length scale do form. We present a simple theory which determines the parameter values for which they do and which also provides scaling laws for the zones' velocities and widths. Thus we are able to adjust the widths and strengths of the zonal flows by changing the forcing and dissipation rates properly. We discuss the implications for Jupiter, compare the numerical experiments with similar ones carried out previously by others, and show how one could build a laboratory experiment that would form jovian-like winds with two easily adjustable control parameters that determine their widths and strengths.
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