Odd gravitational harmonics of Jupiter: Effects of spherical versus nonspherical geometry and mathematical smoothing of the equatorially antisymmetric zonal winds across the equatorial plane

Abstract

Unlike the even gravitational coefficients of Jupiter that are caused by both the rotational distortion and the equatorially symmetric zonal winds, the odd jovian gravitational coefficients are directly linked to the depth of the equatorially antisymmetric zonal winds. Accurate estimation of the wind-induced odd coefficients and comparison with measurements of those coefficients would be key to understanding the structure of the zonal winds in the deep interior of Jupiter. We consider two problems in connection with the jovian odd gravitational coefficients. In the first problem, we show, by solving the governing equations for the northern hemisphere of Jupiter subject to an appropriate condition at the equatorial plane, that the effect of non-spherical geometry makes an insignificant contribution to the lowermost- order odd gravitational coefficients. In the second problem, we investigate the effect of the equatorial smoothing used to avoid the discontinuity in the winds across the equatorial plane when the thermal wind equation is adopted to compute the odd gravitational coefficients. We reveal that, because of the dominant effect of the equatorial smoothing, the odd gravitational coefficients so obtained for deep zonal winds do not reflect physically realistic dynamics taking place in the deep interior of Jupiter.