Interaction of magnetic field and flow in the outer shells of giant planets

This study of the interaction of magnetic field and flow in the outer shells of giant planets consists of three parts.; Part one. The atmospheres of Jupiter and Saturn exhibit strong and stable zonal winds. Busse suggested that they might be the surface expression of deep flows on cylinders. However, the deep flow hypothesis experiences difficulty when account is taken of the electrical conductivity of molecular hydrogen as measured in shockwave experiments. The deep zonal flow of an electrically conducting fluid would produce a toroidal magnetic field, an associated poloidal electrical current, and Ohmic dissipation. In steady state, the total Ohmic dissipation cannot exceed the planet's net luminosity. If we assume that the observed zonal flow penetrates along cylinders until it is truncated to (near) zero at some spherical radius, the upper bound on Ohmic dissipation constrains this radius to be no smaller than 0.95 Jupiter radius and 0.87 Saturn radius. The truncation of the cylindrical flow in the convective envelope requires an appropriate force to break the Taylor-Proudman constraint. We have been unable to identify any plausible candidate. Thus we conclude that deep-seated cylindrical flows do not exist.; Part two. A fluid shell with sufficient electrical conductivity and azimuthal velocity shear outside of the dynamo generation region can attenuate the non-axisymmetric component of the magnetic field. However, the interaction of the axisymmetric component of the magnetic field and the zonal flow is able to reduce the magnitude of zonal flow. The dimensionless number characterizing this reduction is the Chandrasekhar number. The smaller Saturnian field may allow a larger velocity shear and a greater attenuation of the non-axisymmetric field, thereby providing a possible explanation for the nearly axisymmetric field.; Part three. Combining the study for the attenuation effect produced by the semiconducting layer and the observation of the magnetic field by Galileo and Voyager, we find the possible outer boundary of the dynamo generation zone is at 0.86 Jupiter radius. The magnetic fields generated in the outer shell are dictated by a length scale comparable to the scale height of electrical conductivity, which is much smaller than the radius of the planet.