Hydromagnetic constraints on deep zonal flow in the giant planets

A simple model of the equatorial zonal jet in the giant planets is studied in which the flow is assumed uniform on cylinders concentric with the spin axis, and viscous and magnetic torques on each cylinder are balanced. This 'Taylor constraint' is solved simultaneously with the dynamo equation to obtain the velocity and magnetic field in the equatorial plane. The model is used to reproduce the widely differing jet widths of Jupiter and Saturn eddy viscosity of 2500 sq cm/s. For Saturn, the model has a large magnetic Reynolds number where the Chandrasekhar number Q = 1, and hence exhibits substantial axisymmetrization of the field in the equatorial plane.