Impact of the Core Deformation on the Tidal Heating and Flow in Enceladus' Subsurface Ocean

Abstract

We present a novel approach to modeling the tidal response of icy moons with subsurface oceans. The problem is solved in the time domain and the flow in the ocean is calculated simultaneously with the deformation of the core and the ice shell. To simplify the calculations, we assume that the internal density interfaces are spherical and the effective viscosity of water is equal to or greater than 100 Pa s. The method is used to study the effect of an unconsolidated core on tidal dissipation in Enceladus' ocean. We show that the partitioning of tidal heating between the core and the ocean strongly depends on the thickness of the ocean layer. If the ocean thickness is significantly greater than 1 km, heat production is dominated by tidal dissipation in the core and the amount of heat produced in the ocean is negligible. In contrast, when the ocean thickness is less than about 1 km, tidal heating in the core diminishes and dissipation in the ocean increases, leaving the total heat production unchanged. Extrapolation of our results to realistic conditions indicates that tidal flow is turbulent which suggests that the linearized Navier-Stokes equation may not be appropriate for modeling the tidal response of icy moons. Finally, we compare our results with those obtained by solving the Laplace tidal equations and discuss the limitations of the two-dimensional models of ocean circulation.