Ocean Tidal Dynamics and Dissipation in the Thick Shell Worlds

Tidal dissipation in the subsurface oceans of icy satellites has so far only been explored in the limit of a free-surface ocean or under the assumption of a thin ice shell. Here we consider ocean tides in the opposite limit, under the assumption of an infinitely rigid, immovable, ice shell. This assumption forces the surface displacement of the ocean to remain zero, and requires the solution of a pressure correction to ensure that the ocean is mass conserving (divergence-free) at all times. This work investigates the effect of an infinitely rigid lid on ocean dynamics and dissipation, focusing on implications for the thick shell worlds Ganymede and Callisto. We perform simulations using a modified version of the numerical model Ocean Dissipation in Icy Satellites (ODIS), solving the momentum equations for incompressible shallow water flow under a degree-2 tidal forcing. The velocity solution to the momentum equations is updated iteratively at each time-step using a pressure correction to guarantee mass conservation everywhere, following a standard solution procedure originally used in solving the incompressible Navier-Stokes equations. We reason that any model that investigates ocean dynamics beneath a global ice layer should be tested in the limit of an immovable ice shell and must yield solutions that exhibit divergence-free flow at all times.