THERMAL-GRAVITATIONAL WIND EQUATION FOR THE WIND-INDUCED GRAVITATIONAL SIGNATURE OF GIANT GASEOUS PLANETS: MATHEMATICAL DERIVATION, NUMERICAL METHOD, AND ILLUSTRATIVE SOLUTIONS
- Center for Geophysical and Astrophysical Fluid Dynamics and Department of Mathematical Sciences, University of Exeter, Exeter, EX4 4QF (United Kingdom)
- Center for Geophysical and Astrophysical Fluid Dynamics, University of Exeter, Exeter, EX4 4QF (United Kingdom)
- Department of Earth, Planetary and Space Sciences, University of California, Los Angeles, CA 90095-1567 (United States)
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 thermal-gravitational 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.
- OSTI ID:
- 22522244
- Journal Information:
- Astrophysical Journal, Vol. 806, Issue 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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