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Register a new userDiffering Enceladean ocean circulation and ice shell geometries driven by tidal heating in the ice versus the core
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Beneath the icy shell encasing Enceladus, a small icy moon of Saturn, a global ocean of liquid water ejects geyser-like plumes into space through fissures in the ice, making it an attractive place to investigate habitability and to search for extraterrestrial life. The existence of an ocean on Enceladus has been attributed to the heat generated in dissipative processes associated with deformation by tidal forcing. However, it remains unclear whether that heat is mostly generated in its ice shell or silicate core. Answering this question is crucial if we are to unravel patterns of ocean circulation and tracer transport that will impact both the habitability of Enceladus and our ability to interpret putative evidence of any habitability and/or life. Using a nonhydrostatic ocean circulation model, we describe and contrast the differing circulation patterns and implied ice shell geometries to be expected as a result of heating in the ice shell above and heating in the core below Enceladus ocean layer. If heat is generated primarily in the silicate core we would predict enhanced melting rates at the equator. In contrast, if heat is primarily generated in the ice shell we would infer a poleward-thinning ice geometry consistent with Cassini Mission observations.
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Of profound astrobiological interest is that not only does Enceladus have a water ocean, but it also appears to be salty, important for its likely habitability. Here, we investigate how salinity affects ocean dynamics and equilibrium ice shell geometry and use knowledge of ice shell geometry and tidal heating rates to help constrain ocean salinity. We show that the vertical overturning circulation of the ocean, driven from above by melting and freezing and the temperature dependence of the freezing point of water on pressure, has opposing signs at very low and very high salinities. In both cases, heat and freshwater converges toward the equator, where the ice is thick, acting to homogenize thickness variations. In order to maintain observed ice thickness variations, ocean heat convergence should not overwhelm heat loss rates through the equatorial ice sheet. This can only happen when the oceans salinity has intermediate values, order $20$~psu. In this case polar-sinking driven by meridional temperature variations is largely canceled by equatorial-sinking circulation driven by salinity variations and a consistent ocean circulation, ice shell geometry and tidal heating rate can be achieved.
Atmospheric circulation patterns derived from multi-spectral remote sensing can serve as a guide for choosing a suitable entry site for a future in situ probe mission. Since the Voyager-2 flybys in the 1980s, three decades of observations from ground- and space-based observatories have generated a picture of Ice Giant circulation that is complex, perplexing, and altogether unlike that seen on the Gas Giants. This review seeks to reconcile the various competing circulation patterns from an observational perspective, accounting for spatially-resolved measurements of: zonal albedo contrasts and banded appearances; cloud-tracked zonal winds; temperature and para-H$_2$ measurements above the condensate clouds; and equator-to-pole contrasts in condensable volatiles (methane and hydrogen sulphide) in the deeper troposphere. These observations identify three distinct latitude domains: an equatorial domain of deep upwelling and upper-tropospheric subsidence, potentially bounded by peaks in the retrograde zonal jet and analogous to Jovian cyclonic belts; a mid-latitude transitional domain of upper-tropospheric upwelling, vigorous cloud activity, analogous to Jovian anticyclonic zones; and a polar domain of strong subsidence, volatile depletion, and small-scale (and potentially seasonally-variable) convective activity. Taken together, the multi-wavelength observations suggest a tiered structure of stacked circulation cells (at least two in the troposphere and one in the stratosphere), potentially separated in the vertical by (i) strong molecular weight gradients associated with cloud condensation, and by (ii) transitions from a thermally-direct circulation regime at depth to a wave-driven circulation regime at high altitude. The inferred circulation can be tested in the coming decade by 3D simulations and by observations from future world-class facilities. [Abridged]
As a long-term energy source, tidal heating in subsurface oceans of icy satellites can influence their thermal, rotational, and orbital evolution, and the sustainability of oceans. We present a new theoretical treatment for tidal heating in thin subsurface oceans with overlying incompressible elastic shells of arbitrary thickness. The stabilizing effect of an overlying shell damps ocean tides, reducing tidal heating. This effect is more pronounced on Enceladus than on Europa because the effective rigidity on a small body like Enceladus is larger. For the range of likely shell and ocean thicknesses of Enceladus and Europa, the thin shell approximation of Beuthe (2016) is generally accurate to less than about 4%.The time-averaged surface distribution of ocean tidal heating is distinct from that due to dissipation in the solid shell, with higher dissipation near the equator and poles for eccentricity and obliquity forcing respectively. This can lead to unique horizontal shell thickness variations if the shell is conductive. The surface displacement driven by eccentricity and obliquity forcing can have a phase lag relative to the forcing tidal potential due to the delayed ocean response. For Europa and Enceladus, eccentricity forcing generally produces greater tidal amplitudes due to the large eccentricity values relative to the obliquity values. Despite the small obliquity values, obliquity forcing generally produces larger phase lags due to the generation of Rossby-Haurwitz waves. If Europas shell and ocean are respectively 10 and 100 km thick, the tide amplitude and phase lag are 26.5 m and $<1$ degree for eccentricity forcing, and $<2.5$ m and $<18$ degrees for obliquity forcing. Measurement of the obliquity phase lag (e.g. by Europa Clipper) would provide a probe of ocean thickness
We performed numerical simulations of impact crater formation on Europa to infer the thickness and structure of its ice shell. The simulations were performed using iSALE to test both the conductive ice shell over ocean and the conductive lid over warm convective ice scenarios for a variety of conditions. The modeled crater depth-diameter is strongly dependent on thermal gradient and temperature of the warm convective ice. Our results indicate that both a fully conductive (thin) shell and a conductive-convective (thick) shell can reproduce the observed crater depth-diameter and morphologies. For the conductive ice shell over ocean, the best fit is an approximately 8 km thick conductive ice shell. Depending on the temperature (255 - 265 K) and therefore strength of warm convective ice, the thickness of the conductive ice lid is estimated at 5 - 7 km. If central features within the crater, such as pits and domes, form during crater collapse, our simulations are in better agreement with the fully conductive shell (thin shell). If central features form well after the impact, however, our simulations suggest a conductive-convective shell (thick shell) is more likely. Although our study does not provide firm conclusion regarding the thickness of Europas ice shell, our work indicates that Valhalla-class multiring basins on Europa may provide robust constraints on the thickness of Europas ice shell.
We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from where various types of spiral patterns can be generated and their evolution and stability in time analyzed. By restricting the nonlinear system of equations to its quadratic terms we obtain swirl solutions emphasizing logarithmic spiral geometry. The resulting solutions are analyzed and validated using three mathematical approaches: one predicting the formation of patterns as Townes solitary modes, another approach mapping the nonlinear system into a sine-Gordon equation, and a third approach uses a series expansion. Pure radial, azimuthal and spiral modes are obtained from the fully nonlinear equations. Combinations of multiple-spiral solutions are also obtained, matching the experimental observations. The nonlinear stability of the spiral patterns is analyzed by Arnolds convexity method, and the Hamiltonian of the solutions is plotted versus some order parameters showing the existence of geometric phase transitions.
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