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Motion in the Interiors and Atmospheres of Jupiter and Saturn: Scale Analysis, Anelastic Equations, Barotropic Stability Criterion

Ingersoll, Andrew P. and Pollard, David (1982) Motion in the Interiors and Atmospheres of Jupiter and Saturn: Scale Analysis, Anelastic Equations, Barotropic Stability Criterion. Icarus, 52 (1). pp. 62-80. ISSN 0019-1035. doi:10.1016/0019-1035(82)90169-5.

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If Jupiter's and Saturn's fluid interiors were inviscid and adiabatic, any steady zonal motion would take the form of differentially rotating cylinders concentric about the planetary axis of rotation. B. A. Smith et al. [Science215, 504–537 (1982)] showed that Saturn's observed zonal wind profile extends a significant distance below cloud base. Further extension into the interior occurs if the values of the eddy viscosity and superadiabaticity are small. We estimate these values using a scaling analysis of deep convection in the presence of differential rotation. The differential rotation inhibits the convection and reduces the effective eddy viscosity. Viscous dissipation of zonal mean kinetic energy is then within the bounds set by the internal heat source. The differential rotation increases the superadiabaticity, but not so much as to eliminate the cylindrical structure of the flow. Very large departures from adiabaticity, necessary for decoupling the atmosphere and interior, do not occur. Using our scaling analysis we develop the anelastic equations that describe motions in Jupiter's and Saturn's interiors. A simple problem is solved, that of an adiabatic fluid with a steady zonal wind varying as a function of cylindrical radius. Low zonal wavenumber perturbations are two dimensional (independent of the axial coordinate) and obey a modified barotropic stability equation. The parameter analogous to β is negative and is three to four times larger than the β for thin atmospheres. Jupiter's and Saturn's observed zonal wind profiles are close to marginal stability according to this deep sphere criterion, but are several times supercritical according to the thin atmosphere criterion.

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Ingersoll, Andrew P.0000-0002-2035-9198
Additional Information:© 1982 by Academic Press, Inc. Received January 25, 1982; revised June 7, 1982. We have benefited from comments by David J. Stevenson, F. H. Busse, Raymond Hide, and two anonymous referees. This research was supported by the NASA Planetary Atmospheres Program under Grant NAGW-58. Contribution 3729 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125.
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Caltech Division of Geological and Planetary Sciences3729
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Official Citation:Andrew P. Ingersoll, David Pollard, Motion in the interiors and atmospheres of Jupiter and Saturn: scale analysis, anelastic equations, barotropic stability criterion, Icarus, Volume 52, Issue 1, October 1982, Pages 62-80, ISSN 0019-1035, 10.1016/0019-1035(82)90169-5. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35834
Deposited By: Ruth Sustaita
Deposited On:05 Dec 2012 22:48
Last Modified:09 Nov 2021 23:18

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