  How deep do Saturn's zonal winds penetrate below the cloud-level has been a
decades-long question, with important implications not only for the atmospheric
dynamics, but also for the interior density structure, composition, magnetic
field and core mass. The Cassini Grand Finale gravity experiment enables
answering this question for the first time, with the premise that the planet's
gravity harmonics are affected not only by the rigid body density structure but
also by its flow field. Using a wide range of rigid body interior models and an
adjoint based thermal wind balance, we calculate the optimal flow structure
below the cloud-level and its depth. We find that with a wind profile, largely
consistent with the observed winds, when extended to a depth of around 8,800
km, all the gravity harmonics measured by Cassini are explained. This solution
is in agreement with considerations of angular momentum conservation, and is
consistent with magnetohydrodynamics constraints.
