An Analytical Method for the Internal Structure and Gravitational Signature of Deep Zonal Flows in Jupiter-like Planets

摘要

If zonal winds at the cloud level of giant gaseous planets like Jupiter and Saturn manifest their deep interior dynamics,the density anomaly associated with the winds produces a gravitational signature that can be used to probe and constrain the interior structure, fluid motion and convective dynamo processes. We review a new analytical method, based on a self-consistent perturbation approach using the oblate spheroidal wave function, for studying the internal structure and the gravitational signature of deep zonal flows in Jupiter-like planets. In the perturbation approach, the leading-order solution accounts for rotational distortion and determines the non-spherical shape, internal structure and gravitational field in hydrostatic equilibrium. The next-order solution, which is mathematically and physically coupled with the leading-order solution, describes the gravitational signature caused by the zonal flows. We also apply the analytical method to a generic Jupiter-like planet and compare the analytical solution with the corresponding three-dimensional numerical solution based on a finite element method.