Thin-shell Tidal Dynamics of Ocean Worlds

Abstract

Several solar system moons harbor subsurface water oceans; extreme internal heating or solar irradiation can form magma oceans in terrestrial bodies. Tidal forces drive ocean currents, producing tidal heating that affects the thermal−orbital evolution of these worlds. If the outermost layers (ocean and overlying shell) are thin, tidal dynamics can be described using thin-shell theory. Previous work assumed that the ocean and shell's thickness and density are uniform. We present a formulation of thin-shell dynamics that relaxes these assumptions and apply it to several cases of interest. The tidal response of unstratified oceans of constant thickness is given by surface gravity and Rossby waves, which can resonate with the tidal force. The oceans of the outer solar system are too thick for gravity wave resonances, but high-amplitude Rossby waves can be excited in moons with high orbital obliquity. We find that meridional ocean thickness variations hinder the excitation of Rossby waves, decreasing tidal dissipation and increasing the inclination damping timescale, which allows us to reconcile the present inclination of the Moon with the existence of a past long-lived magma ocean and to explain the inclination of Titan and Callisto without invoking a recent excitation. Stratified oceans can support internal gravity waves. We show that dissipation due to internal waves can exceed that resulting from surface gravity waves. For Enceladus, it can be close to the moon’s thermal output, even if the ocean is weakly stratified. Shear due to internal waves can result in Kelvin–Helmholtz instabilities and induce ocean mixing.