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[45.03] Constraints on the Observed Zonal Flows from the Magnetic Fields in Giant Planets

J.J. Liu, D.J. Stevenson (Division of Geological and Planetary Sciences, California Institute of Technology)

The zonal winds on the surface of the giant planets are very strong (~100m/s ) and stable (on a decadal time scale). Observations by the Galileo probe suggest that the zonal flow might be deep seated. However, the magnitude of the zonal flow must be reduced to a small value in the interior of the giant planets because the flow is defined relative to the magnetic field frame of reference (System III) and very large zonal flows can not be tolerated in a high conductivity region. The mechanisms for reducing the magnitude of the zonal flow and the coupling between the zonal flow and magnetic field are unclear. Here we use a coupled Navier-Stokes equation and the magnetic induction equation in steady state to study this.

From Navier-Stokes, we find that the zonal flow v_th can be expressed in three parts: v_th(s,z) = a(s) + B_th²/4\mu₀\rho\Omega s + F(grad(\rho),B_th)/4\mu₀\rho\Omega s, where a(s) is an arbitrary function of cylindrical radius (s) only, z is the coordinate parallel to the rotation axis, B_th is the toroidal field, \mu₀ is the permeability of free space, \rho(s,z) is the density, \Omega is the planetary rotation and F is a function of the density gradient (grad(\rho)) and the toroidal magnetic field. The first part is the geostrophic flow consistent with the Taylor-Proudman theorem. The second part is due to the tensile force that arises from the curvature of the toroidal field, and always leads a prograde flow. The third part comes from the density variation and meridional gradient of the toroidal field, and may lead to the prograde flow or the retrograde flow. Whether the flow observed on the surface could be reduced to small values in the interior will depend on the direction of the flow, the density gradient and also the structure of the toroidal magnetic field. It can also be shown that the magnitude of the generated toroidal magnetic field in the interior of the giant planets is very large and around 10 Tesla for consistency with the observed zonal flow on the surface of the giant planets.

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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.