Ice and Fluid Dynamics

Abstract:

Enceladus is a target for astrobiology due to the (Formula presented.) plume ejecta measured by the Cassini spacecraft and the inferred subsurface ocean that could be the source of the geysers. Here we explore an alternative where shear heating along tiger stripe fractures produces partial melting in the ice shell and interstitial convection allows fluid to be ejected as geysers. We use an idealized two-dimensional reactive transport model to simulate a mushy region generated by an upper-bound estimate for the localized shear heating rate. We find that the rate of internal melting could potentially match the observed eruption rate. The composition of the liquid brine would be, however, distinct from that of the ocean, due to fractionation during partial melting. This shear heating mechanism for geyser formation could apply to Enceladus and other icy moons and has implications for our understanding of the geophysical processes and astrobiological potential of icy satellites.

Abstract:

We model transient mushy-layer growth for a binary alloy solidifying from a cooled boundary, characterising the impact of liquid composition and thermal growth conditions on the mush porosity and growth rate. We consider cooling from a perfectly conducting isothermal boundary, and from an imperfectly conducting boundary governed by a linearised thermal boundary condition. For an isothermal boundary we characterise different growth regimes depending on a concentration ratio, which can also be viewed as characterising the ratio of composition-dependent freezing point depression versus the temperature difference across the mushy layer. Large concentration ratio leads to high porosity throughout the mushy layer and an asymptotically simplified model for growth with an effective thermal diffusivity accounting for latent heat release from internal solidification. Low concentration ratio leads to low porosity throughout most of the mushy layer, except for a high-porosity boundary layer localised near the mush–liquid interface. We identify scalings for the boundary-layer thickness and mush growth rate. An imperfectly conducting boundary leads to an initial lag in the onset of solidification, followed by an adjustment period, before asymptoting to the perfectly conducting state at large time. We develop asymptotic solutions for large concentration ratio and large effective heat capacity, and characterise the mush structure, growth rate and transition times between the regimes. For low concentration ratio the high porosity zone spans the full mush depth at early times, before localising near the mush–liquid interface at later times. Such variation of porosity has important implications for the properties and biological habitability of mushy sea ice.

Abstract:

We study linear convective instability in a mushy layer formed by solidification of a binary alloy, cooled by either an isothermal perfectly conducting boundary or an imperfectly conducting boundary where the surface temperature depends linearly on the surface heat flux. A companion paper (Hitchen & Wells, J. Fluid Mech., 2025, in press) showed how thermal and salinity conditions impact mush structure. We here quantify the impact on convective instability, described by a Rayleigh number characterising the ratio of buoyancy to dissipative mechanisms. Two limits emerge for a perfectly conducting boundary. When the salinity-dependent freezing-point depression is large versus the temperature difference across the mush, convection penetrates throughout the depth of a high-porosity mush. The other limit, which we will call the Stefan limit, has small freezing-point depression and inhibits convection, which localises at onset to a high-porosity boundary layer near the mush–liquid interface. Scaling arguments characterise variation of the critical Rayleigh number and wavenumber based on the potential energy contained in order-one aspect ratio convective cells over the high-porosity regions. The Stefan number characterises the ratio of latent and sensible heats, and has moderate impact on stability via modification of the background temperature and porosity. For imperfectly conducting boundaries, the changing surface temperature causes stability to decrease over time in the limit of large freezing-point depression, but in the Stefan limit combines with the decreasing porosity to yield non-monotonic variation of the critical Rayleigh number. We discuss the implications for convection in growing sea ice.