Abstract
We present a two-phase model for the generation of meltwater and its propagation through the outer shells of icy satellites such as Europa, Enceladus or Titan. We exploit the analogy with the process of partial melt generation in the Earth's interior by adopting the formalism of two-phase flow developed in the mantle-dynamics community, and by means of scaling analysis we derive a reduced system appropriate for our planetary application.
The resultant system couples Darcy's law with the deformation of the viscous ice matrix. We numerically investigate the system in a simplified one-dimensional geometry, corresponding to a laterally uniform ice layer, and analyze the role of various physical parameters.
We focus on the leading-order effects, namely (i) the key importance of ice permeability, (ii) the role of complex ice rheology depending on temperature, deformation mechanisms and water content, (iii) the possible contribution of surface tension and (iv) the effects of mechanical coupling between the phases. Our analysis suggests that the global water transport through temperate ice is mainly controlled by ice permeability and can be well approximated by a model in which the complex ice rheology is parameterized in terms of a constant viscosity.
While the mechanical coupling between the phases dramatically affects the flow at the local scale, the surface tension appears to be insignificant.