Gravitational signature of rotationally distorted Jupiter caused by deep zonal winds

Both deep zonal winds, if they exist, and the basic rotational distortion of Jupiter contribute to its zonal gravity coefficients Jn for n ⩾ 2. In order to capture the gravitational signature of Jupiter that is caused solely by its deep zonal winds, one must take into account the full effect of rotational distortion by computing the coefficients Jn in non-spherical geometry. This represents a difficult and challenging problem because the widely-used spherical-harmonic-expansion method becomes no longer suitable. Based on the model of a polytropic Jupiter with index unity, we compute Jupiter's gravity coefficients J2, J4, J6, … , J12 taking into account the full effect of rotational distortion of the gaseous planet using a finite element method. For the model of deep zonal winds on cylinders parallel to the rotation axis, we also compute the variation of the gravity coefficients ΔJ2, ΔJ4, ΔJ6, … , ΔJ12 caused solely by the effect of the winds in non-spherical geometry. It is found that the effect of the zonal winds on lower-order coefficients is weak, ∣ΔJn/Jn∣ < 1%, for n = 2, 4, 6, but it is substantial for the high-degree coefficients with n ⩾ 8.