Thermal-gravitational wind equation for the wind-induced gravitational signature of giant gaseous planets: mathematical derivation, numerical method, and illustrative solutions
American Astronomical Society
The standard thermal wind equation (TWE) relating the vertical shear of a flow to the horizontal density gradient in an atmosphere has been used to calculate the external gravitational signature produced by zonal winds in the interiors of giant gaseous planets. We show, however, that in this application the TWE needs to be generalized to account for an associated gravitational perturbation. We refer to the generalized equation as the thermalgravitational wind equation (TGWE). The generalized equation represents a two-dimensional kernel integral equation with the Green’s function in its integrand and is hence much more difficult to solve than the standard TWE. We develop an extended spectral method for solving the TGWE in spherical geometry. We then apply the method to a generic gaseous Jupiter-like object with idealized zonal winds. We demonstrate that solutions of the TGWE are substantially different from those of the standard TWE. We conclude that the TGWE must be used to estimate the gravitational signature of zonal winds in giant gaseous planets.
© 2015. The American Astronomical Society. All rights reserved. Received 26 February 2015, accepted for publication 4 May 2015 Published 23 June 2015
Please cite the published version available at DOI: 10.1088/0004-637X/806/2/270
Vol. 806, pp. 270 - 279