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

Tidal forces generate time-varying currents in bodies with fluid layers, such as the icy ocean moons of the outer solar system. The expectation has been that tidal currents are periodic—they average to zero over a forcing period—so that they are not associated with a mean flow. This expectation arises from the assumption of linearity. Here, we relax this assumption and develop a theory that predicts the emergence of mean currents driven by any periodic forcing. The theory, derived in the context of a global, uniform, shallow ocean, constitutes a set of mean flow equations forced by non-linear eddy fluctuations. The latter are the canonical, periodic tidal currents predicted by the Laplace Tidal equations. We show that the degree-2 tide-raising potential due to obliquity and/or orbital eccentricity can drive time-averaged currents with zonal wavenumbers from 0 to 4. The most prominent of these is a retrograde zonal jet driven by the obliquity-forcing potential. Assuming Cassini state obliquities, this jet has speeds ranging from 0.01 to 1 mm s⁻¹, which can exert torques up to roughly 10¹⁵ N m at the ice–ocean interfaces of Europa, Callisto, Titan, and Triton. Depending on the viscosity of the ice shell, these torques could drive ice shell drift rates of tens to potentially hundreds of meters a year. Thinner or stably stratified global oceans can experience much faster mean currents.