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Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation

Cao, Hao and Stevenson, David J. (2017) Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation. Journal of Geophysical Research. Planets, 122 (4). pp. 686-700. ISSN 2169-9097. doi:10.1002/2017JE005272.

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Any nonspherical distribution of density inside planets and stars gives rise to a nonspherical external gravity and change of shape. If part or all of the observed zonal flows at the cloud deck of Jupiter and Saturn represent deep interior dynamics, then the density perturbations associated with the deep zonal flows could generate gravitational signals detectable by the Juno mission and the Cassini Grand Finale. Here we present a critical examination of the applicability of the thermal wind equation to calculate the wind-induced gravity moments. Our analysis shows that wind-induced gravity moments calculated from the thermal wind equation (TWE) are in overall agreement with the full solution to the Euler equation. However, the accuracy of individual high-degree moments calculated from TWE depends crucially on retaining the nonsphericity of the background density and gravity. Only when the background nonsphericity of the planet is taken into account does the TWE make accurate enough prediction (with a few tens of percent errors) for individual high-degree gravity moments associated with deep zonal flows. Since the TWE is derived from the curl of the Euler equation and is a local relation, it necessarily says nothing about any density perturbations that contribute irrotational terms to the Euler equation and that have a nonlocal origin. However, the predicted corrections from these density contributions to the low harmonic degree gravity moments are not discernible from insignificant changes in interior models, while the corrections at high harmonic degree are very small, a few percent or less.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Cao, Hao0000-0002-6917-8363
Stevenson, David J.0000-0001-9432-7159
Additional Information:© 2017 American Geophysical Union. Received 19 JAN 2017; Accepted 18 MAR 2017; Accepted article online 27 MAR 2017; Published online 18 APR 2017. This work has been supported by NASA’s Juno mission. All relevant data are listed in the tables and in the manuscript. We thank the two reviewer for their constructive comments.
Group:Astronomy Department
Funding AgencyGrant Number
Subject Keywords:Giant Planets; Gravity; Zonal Flows; Thermal Wind Equation; Euler Equation
Issue or Number:4
Record Number:CaltechAUTHORS:20150914-082857268
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Official Citation:Cao, H., and D. J. Stevenson (2017), Gravity and zonal flows of giant planets: From the Euler equation to the thermal wind equation, J. Geophys. Res. Planets, 122, 686–700, doi:10.1002/2017JE005272
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60210
Deposited By: Tony Diaz
Deposited On:14 Sep 2015 18:32
Last Modified:10 Nov 2021 22:31

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