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.

Tidal Heating in a Subsurface Magma Ocean on Io Revisited

“…Although their method is similar at first glance to our approach, it differs from it in that the boundaries of the ocean are treated as free‐slip surfaces and the flow velocity does not change with radius. As recently shown by Aygün and Čadek (2023b), the method by Beuthe (2016) correctly predicts the radially averaged flow in a thin ocean layer but can lead to biased estimates of tidal heating. Unlike Beuthe (2016), Rovira‐Navarro et al.…”

“…(2019) determine the dissipation rate in the ocean by using the 3D Navier‐Stokes equations, but assume that the deformation of the crust is not affected by the flow in the ocean and can therefore be imposed as a boundary condition at the surface of the ocean. However, this assumption is valid only if the thickness of the ocean layer is greater than about 0.01 R m ≈ 15 km, that is, outside the thickness range considered in the present study (Aygün & Čadek, 2023b).…”

“…Equations 1-3 are solved in the time domain using the semi-spectral method developed by Aygün and Čadek (2023b). The spherical harmonic expansions are truncated at degree 20-200 depending on the viscosity of the magma ocean, while the spherical harmonic coefficients are discretized in 800 unevenly spaced radial points.…”

“…Although their method is similar at first glance to our approach, it differs from it in that the boundaries of the ocean are treated as free-slip surfaces and the flow velocity does not change with radius. As recently shown by Aygün and Čadek (2023b), the method by Beuthe (2016) 2019) determine the dissipation rate in the ocean by using the 3D Navier-Stokes equations, but assume that the deformation of the crust is not affected by the flow in the ocean and can therefore be imposed as a boundary condition at the surface of the ocean. However, this assumption is valid only if the thickness of the ocean layer is greater than about 0.01R m ≈ 15 km, that is, outside the thickness range considered in the present study (Aygün & Čadek, 2023b).…”

Tidal Forcing in Icy‐Satellite Oceans Drives Mean Circulation and Ice‐Shell Torques

“…The LTE are roughly valid provided that the thickness of the ocean layer is less than 5% to 10% of the body's radius. This is an acceptable assumption for many of the ocean worlds considered here, with the notable exception of Enceladus (Aygün & Čadek, 2023) and probably Dione. The shallow water assumption precludes the emergence of internal, inertial tidal waves (Rekier et al, 2019;Rovira-Navarro et al, 2019), which would be another manifestation of time-averaged currents, though this is unlikely to affect the results here.…”