Ohmic Dissipation Constraint on Deep-seated Zonal Winds in Jupiter and Saturn

Details Ohmic Dissipation Constraint on Deep-seated Zonal Winds in Jupiter and Saturn Ohmic Dissipation Constraint on Deep-seated Zonal Winds in Jupiter and Saturn

Sep 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dps....38.0205l&link_type=abstract

American Astronomical Society, DPS meeting #38, #02.05; Bulletin of the American Astronomical Society, Vol. 38, p.483

Astronomy and Astrophysics

Astronomy

Scientific paper

The atmospheres of Jupiter and Saturn exhibit strong and stable zonal winds. Busse (1976) suggested that they might be the surface expression of deep flows on cylinders. This 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 0.96 Jupiter radius and 0.86 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. The Lorentz force is much too weak. Order of magnitude considerations suggest that both divergence of the Reynolds stress and the buoyancy force are inadequate. Therefore, we claim that the assumed deep-seated flows do not exist. Equatorial jets could maintain constant velocities on cylinders through the planet provided their half-widths were no greater than 21° for Jupiter and 31° for Saturn. These boundaries are similar to those of the equatorial jets observed in the planets’ atmospheres. We speculate that the Reynolds stress associated with turbulent convection promotes differential rotation throughout the interiors of the giant planets. Along cylinders that pass through the maximum penetration depth, the Maxwell stress balances the Reynolds stress resulting in small differential rotation except in the stably stratified atmosphere. Equatorial jets are unencumbered by the Maxwell stress. They pass through the planets and maintain velocities limited by parasitic instabilities.

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