Tidal heating can play an important role in the formation and evolution of subsurface oceans of outer-planet moons. Up until now tidal heating has only been studied in subsurface oceans of spatially uniform thickness. We develop a numerical model to consider oceans of spatially variable thickness. We use the Laplace Tidal Equations for the ocean and model the ice shell using membrane theory. The problem is solved using the commercial Finite Element software Comsol Multiphysics®. We use this new model to study the tidal response of Enceladus' ocean with a twofold objective: to understand how ocean thickness variations modify the tidal response of a subsurface ocean and to assess if tidal dissipation in an Enceladan ocean with varying ocean thickness can explain the high heat flux emanating from Enceladus' South Polar Terrain and the perdurance of a subsurface ocean. We consider the effect of meridional ocean thickness changes of spherical harmonic degree two and three as suggested by topography and gravimetry data. We observe that an ocean with degree two topography responds with the same eigenmodes as an ocean of constant thickness but resonances occur for thicker oceans. However, resonant ocean thicknesses are still thin compared to current estimates for Enceladus ocean thickness. Rossby-Haurwitz waves, excited by the obliquity tide for thick oceans of constant thickness, are not excited at the tidal frequency when oceans of variable thickness are considered. This result implies that the role of the obliquity tide in ocean tidal-dissipation might have been overestimated for Enceladus and other icy worlds. An antisymmetric, degree-three ocean thickness variation mixes the ocean modes excited in a constant thickness ocean by the eccentricity and obliquity tide.

Some of the moons of the outer solar system harbour subsurface liquid oceans. Tidal dissipation plays an important role in preventing these oceans from freezing. In the past, most studies considered only tidal dissipation in the solid layers of these bodies (rock and ice). Recently, new studies considering tidal dissipation in the oceans of these moons have appeared. All of them make use of the shallow water approximation. However, the use of this approximation might not be adequate. Here we consider the linear non-hydrostatic three dimensional response of these oceans to tidal forcing with the full Coriolis force. To do so we consider an ocean of homogeneous density contained within a perfectly spherical shell and neglect the effect of the ice shell. We force the ocean with a time changing tidal potential and observe patterns of periodic inertial waves that take energy from the global tidal forcing and focus it along thin shear layers that propagate in the fluid. We focus on Europa and Enceladus, showing that inertial waves result in fluid flows of significant amplitude (a few cm/s). Nevertheless, we find that under the previously mentioned assumptions tidal dissipation due to inertial waves is several orders of magnitude smaller than Europa's radiogenic heating and Enceladus’ observed heat flux. Finally, we propose additional dissipation mechanisms that might play a relevant role in Europa and Enceladus and could be further investigated.