Water-Ice Interactions Driven by Ocean Convection in Jupiter’s Icy Moons

Introduction:  The main reservoirs of liquid water in the Solar System are hidden below the icy surfaces of several moons of the gaseous giants, namely Jupiter and Saturn. None of these Icy Moons (as they are called) are found in the astronomical habitable zone, the zone of a planetary system where liquid water is possible on the surface of a body. However, tidal heating produced by the gaseous giants and internal heating due to radioactive decay in the silicate mantle allow the presence of liquid water oceans in the subsurface that could host the necessary conditions for life to emerge and persist [1,2].
Although these moons are directly accessible by space missions, today’s technology only gives us access to their surfaces, leaving the oceans hidden beneath the icy crust. For several of these worlds, the icy crust appears to be active today (or has been in the past), connecting the ocean to the surface and making orbiter observations even more interesting for understanding the internal oceans. Among these ocean worlds, Jupiter’s icy moons will soon be visited by two orbiters, ESA/ASI JUICE and NASA Europa Clipper. From this perspective, the dynamics of the internal oceans of such satellites have been investigated to better understand water-ice interaction and the possible surface-subsurface connection.

Methods:  Icy moons’ oceans are known to be heated from below, facilitating natural, or Rayleigh-Bénard, convection that could transport enough heat to let the overlaying icy crust undergo phase changes. In this perspective, we explored the (expectedly turbulent) convective dynamics of a portion of the hidden ocean. In this work, we considered a Newtonian fluid layer, set in a 3D box with thickness D and horizontal sides 2πD. Periodic boundary conditions were used along the horizontal axes at x=0, 2πD and y=0, 2πD, while boundary conditions on temperature, salinity, and velocity along the vertical were defined at z=0, z=D. Considering icy moons, at the top of the ocean, a fixed temperature at the ice melting value was considered to maintain the water-ice interface in equilibrium, while at the bottom of the ocean, a fixed heat flux was imposed. Gravity is aligned with the vertical direction, and it points opposite to the z-axis. The model includes rotation that can be set in any direction in the y-z plane. As a first step, for simplicity, the fluid was treated under the Boussinesq approximation, which means that only small density changes were considered so that the equation of state became independent of pressure. In our simulations, only large-scale flows were represented, without resolving the small-scale turbulent motions, which were thus represented in terms of constant eddy viscosity and diffusivity; that is, the kinematic viscosity and the thermal diffusivity were considered as “eddy” quantities. Simulations have been performed with a CFD code [3,4] that solves a system of coupled equations for momentum and temperature in the Boussinesq approximation.

Results: Water-ice interactions were investigated by solving a proper equation that describes the interface between the ocean and the overlaying icy crust, which in non-dimensional units is:

where is the averaged thickness of the ice shell, while H’ is a small perturbation to this average thickness. A and B are constants that depend on the parameters of each moon, such as the internal heat flux, the ocean depth, sea water density, etc. The typical values for these two constants are A~10⁻⁵ and B~ - 1, hence, the evolution of the ice is 10⁻⁵ times slower than that of the ocean.

The equation was numerically solved in two dimensions using the temperature gradient derived from the ocean convection simulations. For Ganymede, the main target of the ESA/ASI JUICE mission, the results indicate that in 10 million years, ocean convection could melt the ice shell (taken to be about 70 km thick, on average [5]) by about 6% (Figure 1). Such topographic variations could be validated in the future by the ESA/ASI-JUICE mission. To better understand the spatial variations of the water-ice interface topography, three-dimensional simulations were performed. In addition, by introducing rotation, it was possible to investigate the effects of convection at different latitudes. Taking horizontal sections of the water-ice interface at the poles, mid-latitudes, and the equator, it was seen that the greatest melting effect is registered at the equator. After 158 years, the maximum melting reaches 0.2 m clustered in a hot spot of about 100 km.

Figure 1: Vertical section of Ganymede’s water-ice interface after 10 million years of ongoing ocean convection.

Figure 2: Horizontal section of Ganymede’s water-ice interface after about 158 years of ongoing ocean convection.

These results could support upcoming missions looking for surface-subsurface connection “hot-spots” on icy satellites.

 References:

[1] Vance S. D. et al. (2014).  Ganymede’s internal structure including thermodynamics of magnesium sulfate oceans in contact with ice. Planetary and Space Science, Vol. 96, Iss. 06. https://doi.org/10.1016/j.pss.2014.03.011

[2] Vance S. D. et al. (2018). Geophysical investigations of habitability in ice-covered ocean worlds. J. Geophys. Res. Planets 123, 180–205. https://doi.org/10.1002/2017JE005341 

[3] Von Hardenberg J. (2008). Large-scale patterns in Rayleigh–Bénard convection, Physics Letters A, Vol. 372, Iss. 13. https://doi.org/10.1016/j.physleta.2007.10.099 

[4] Novi L. et al. (2019). Rapidly rotating Rayleigh-Bénard convection with a tilted axis, Physical Review Vol 99, Iss. 5. https://link.aps.org/doi/10.1103/PhysRevE.99.053116

[5] Soderlund, K. M. (2019). Ocean dynamics of outer solar system satellites. Geophysical Research Letters, 46, 8700–8710. https://doi.org/10.1029/2018GL081880

Additional Information:  This work is part of the JUICE Phase E project, and it was funded by ASI under agreement n. 2023-6-HH.0, CUP F83C23000070005.