Abstract
Recent studies of ocean dynamics suggest that the long-wavelength topography of some icy moons may reflect the phase transitions (melting/freezing) at the interface between the ice shell and the water ocean. Despite the obvious importance of phase changes in the evolution of icy moons, very little is known about how these processes influence their shape, gravity and near-surface stress.
Here we address this issue by performing a series of numerical experiments in which we explore the thermo-mechanical response of an ice layer to heat flux variations imposed at the bottom (phase) boundary. We assume that the heat flux from the ocean consists of two components: the heat flux originating in the deep ocean and associated with the global ocean circulation, and the heat flux due to the flow of water generated by variations in the melting temperature along the deformed ice-water interface.
The effect of salinity on the heat flux from the ocean is neglected. We demonstrate that the mass exchange between the ocean and the ice layer is a natural consequence of the ice-water phase transition and it occurs in both convection and conduction modes, regardless of whether the system is in equilibrium or not.
The magnitude of the heat-flux induced topography strongly depends on the viscosity of ice and the flow of water controlled by the melting temperature. When heat transfer in the ice shell occurs by convection, the surface topography is dominated by small-scale convective features varying in time and its large-scale component does not exceed 10 m.
When the viscosity of the ice shell is high (greater than or similar to 1016 Pa s) and the heat is transferred by conduction, the topography is negatively correlated with the heat flux from the ocean and its amplitude increases with increasing viscosity. Topographic amplitudes comparable to those observed on Titan, Enceladus and Dione are obtained only if the water flow associated with lateral variations in the melting temperature is neglected.
This suggests that this flow may be too weak to reduce the variations in ice shell thickness and the motion of water along the phase boundary is more likely to be controlled by other factors, such as variations in salinity and the presence of non-ice material. In addition, we show that the standard formulation of Airy isostasy can lead to an error of 5%-15% in determining the variations in ice thickness and we propose a new formulation that takes into account the effect of thermal expansion.