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It has been suggested that the ice shell of Jupiter's moon Europa may drift non-synchronously due to tidal torques. Here we argue that torques applied by the underlying ocean are also important and can result in non-synchronous rotation (NSR). The resulting spin rate can be slightly slower than the synchronous angular rate that would have kept the same point of the ice shell facing Jupiter. We develop an ice shell rotation model, driven by ocean stress calculated using a high-resolution state-of-the-art ocean general circulation model, and take into account the viscoelastic deformation of the ice shell. We use the ice shell model results together with observed limits on the ice shell drift speed to constrain ice shell parameters such as effective viscosity, which is currently uncertain by at least four orders of magnitude. Our results suggest, at best, sluggish ice shell convection. Depending on the relaxation time scale of the ice shell and on the ocean currents, the ice shell may exhibit negligible drift, constant drift, or oscillatory drift superimposed on random fluctuations. The expected rotation rate exceeds $\sim$30~m/yr; future spacecraft observations can be used to test these predictions and yield insight into the properties of the ice shell and underlying ocean.

The deep (~100 km) ocean of Europa, Jupiter's moon, covered by a thick icy shell, is one of the most probable places in the solar system to find extraterrestrial life. Yet, its ocean dynamics and its interaction with the ice cover have received little attention. Previous studies suggested that Europa's ocean is turbulent using a global model and taking into account non-hydrostatic effects and the full Coriolis force. Here we add critical elements, including consistent top and bottom heating boundary conditions and the effects of icy shell melting and freezing on ocean salinity. We find weak stratification that is dominated by salinity variations. The ocean exhibits strong transient convection, eddies, and zonal jets. Transient motions organize in Taylor columns parallel to Europa's axis of rotation, are static outside of the tangent cylinder and propagate equatorward within the cylinder. The meridional oceanic heat transport is intense enough to result in a nearly uniform ice thickness, that is expected to be observable in future missions., Comment: There are two animation files associated with the paper: T-surface-movie-d-all.gif, convection-movie-d-all.gif. The paper is in press in Nature Communications

The deep (~100 km) ocean of Europa, Jupiter's moon, covered by a thick icy shell, is one of the most probable places in the solar system to find extraterrestrial life. Yet, its ocean dynamics and its interaction with the ice cover have received little attention. Previous studies suggested that Europa's ocean is turbulent using a global model and taking into account non-hydrostatic effects and the full Coriolis force. Here we add critical elements, including consistent top and bottom heating boundary conditions and the effects of icy shell melting and freezing on ocean salinity. We find weak stratification that is dominated by salinity variations. The ocean exhibits strong transient convection, eddies, and zonal jets. Transient motions organize in Taylor columns parallel to Europa's axis of rotation, are static outside of the tangent cylinder and propagate equatorward within the cylinder. The meridional oceanic heat transport is intense enough to result in a nearly uniform ice thickness, that is expected to be observable in future missions., Comment: There are two animation files associated with the paper: T-surface-movie-d-all.gif, convection-movie-d-all.gif. The paper is in press in Nature Communications

Geological evidence indicates that grounded ice sheets reached sea level at all latitudes during two long-lived Cryogenian (58 and ≥5 My) glaciations. Combined uranium-lead and rhenium-osmium dating suggests that the older (Sturtian) glacial onset and both terminations were globally synchronous. Geochemical data imply that CO2 was 102 PAL (present atmospheric level) at the younger termination, consistent with a global ice cover. Sturtian glaciation followed breakup of a tropical supercontinent, and its onset coincided with the equatorial emplacement of a large igneous province. Modeling shows that the small thermal inertia of a globally frozen surface reverses the annual mean tropical atmospheric circulation, producing an equatorial desert and net snow and frost accumulation elsewhere. Oceanic ice thickens, forming a sea glacier that flows gravitationally toward the equator, sustained by the hydrologic cycle and by basal freezing and melting. Tropical ice sheets flow faster as CO2 rises but lose mass and become sensitive to orbital changes. Equatorial dust accumulation engenders supraglacial oligotrophic meltwater ecosystems, favorable for cyanobacteria and certain eukaryotes. Meltwater flushing through cracks enables organic burial and submarine deposition of airborne volcanic ash. The subglacial ocean is turbulent and well mixed, in response to geothermal heating and heat loss through the ice cover, increasing with latitude. Terminal carbonate deposits, unique to Cryogenian glaciations, are products of intense weathering and ocean stratification. Whole-ocean warming and collapsing peripheral bulges allow marine coastal flooding to continue long after ice-sheet disappearance. The evolutionary legacy of Snowball Earth is perceptible in fossils and living organisms.

Geological evidence indicates that grounded ice sheets reached sea level at all latitudes during two long-lived Cryogenian (58 and ≥5 My) glaciations. Combined uranium-lead and rhenium-osmium dating suggests that the older (Sturtian) glacial onset and both terminations were globally synchronous. Geochemical data imply that CO2 was 102 PAL (present atmospheric level) at the younger termination, consistent with a global ice cover. Sturtian glaciation followed breakup of a tropical supercontinent, and its onset coincided with the equatorial emplacement of a large igneous province. Modeling shows that the small thermal inertia of a globally frozen surface reverses the annual mean tropical atmospheric circulation, producing an equatorial desert and net snow and frost accumulation elsewhere. Oceanic ice thickens, forming a sea glacier that flows gravitationally toward the equator, sustained by the hydrologic cycle and by basal freezing and melting. Tropical ice sheets flow faster as CO2 rises but lose mass and become sensitive to orbital changes. Equatorial dust accumulation engenders supraglacial oligotrophic meltwater ecosystems, favorable for cyanobacteria and certain eukaryotes. Meltwater flushing through cracks enables organic burial and submarine deposition of airborne volcanic ash. The subglacial ocean is turbulent and well mixed, in response to geothermal heating and heat loss through the ice cover, increasing with latitude. Terminal carbonate deposits, unique to Cryogenian glaciations, are products of intense weathering and ocean stratification. Whole-ocean warming and collapsing peripheral bulges allow marine coastal flooding to continue long after ice-sheet disappearance. The evolutionary legacy of Snowball Earth is perceptible in fossils and living organisms.

Geological evidence indicates that grounded ice sheets reached sea level at all latitudes during two long-lived Cryogenian (58 and ≥5 My) glaciations. Combined uranium-lead and rhenium-osmium dating suggests that the older (Sturtian) glacial onset and both terminations were globally synchronous. Geochemical data imply that CO2 was 102 PAL (present atmospheric level) at the younger termination, consistent with a global ice cover. Sturtian glaciation followed breakup of a tropical supercontinent, and its onset coincided with the equatorial emplacement of a large igneous province. Modeling shows that the small thermal inertia of a globally frozen surface reverses the annual mean tropical atmospheric circulation, producing an equatorial desert and net snow and frost accumulation elsewhere. Oceanic ice thickens, forming a sea glacier that flows gravitationally toward the equator, sustained by the hydrologic cycle and by basal freezing and melting. Tropical ice sheets flow faster as CO2 rises but lose mass and become sensitive to orbital changes. Equatorial dust accumulation engenders supraglacial oligotrophic meltwater ecosystems, favorable for cyanobacteria and certain eukaryotes. Meltwater flushing through cracks enables organic burial and submarine deposition of airborne volcanic ash. The subglacial ocean is turbulent and well mixed, in response to geothermal heating and heat loss through the ice cover, increasing with latitude. Terminal carbonate deposits, unique to Cryogenian glaciations, are products of intense weathering and ocean stratification. Whole-ocean warming and collapsing peripheral bulges allow marine coastal flooding to continue long after ice-sheet disappearance. The evolutionary legacy of Snowball Earth is perceptible in fossils and living organisms.

Previous estimates of the annual mean surface temperature of Jupiter's moon, Europa, neglected the effect of the eccentricity of Jupiter's orbit around the Sun, the effect of the emissivity and heat capacity of Europa's ice, the effect of the eclipse of Europa (i.e., the relative time that Europa is within the shadow of Jupiter), the effect of Jupiter's radiation, and the effect of Europa's internal heating. Other studies concentrated on the diurnal cycle but neglected some of the above factors. In addition, to our knowledge, the seasonal cycle of the surface temperature of Europa was not estimated. Here we systematically estimate the diurnal, seasonal and annual mean surface temperature of Europa, when Europa's obliquity, emissivity, heat capacity, and eclipse, as well as Jupiter's radiation, internal heating, and eccentricity, are all taken into account. For a typical internal heating rate of 0.05 W m$^{-2}$, the equator, pole, and the global and mean annual mean surface temperatures are 96K, 46K, and 90K, respectively. We found that the temperature at the high latitudes is significantly affected by the internal heating, especially during the winter solstice, suggesting that measurements of high latitude surface temperatures can be used to constrain the internal heating. We also estimate the incoming solar radiation to Enceladus, the moon of Saturn.

Previous estimates of the annual mean surface temperature of Jupiter's moon, Europa, neglected the effect of the eccentricity of Jupiter's orbit around the Sun, the effect of the emissivity and heat capacity of Europa's ice, the effect of the eclipse of Europa (i.e., the relative time that Europa is within the shadow of Jupiter), the effect of Jupiter's radiation, and the effect of Europa's internal heating. Other studies concentrated on the diurnal cycle but neglected some of the above factors. In addition, to our knowledge, the seasonal cycle of the surface temperature of Europa was not estimated. Here we systematically estimate the diurnal, seasonal and annual mean surface temperature of Europa, when Europa's obliquity, emissivity, heat capacity, and eclipse, as well as Jupiter's radiation, internal heating, and eccentricity, are all taken into account. For a typical internal heating rate of 0.05 W m$^{-2}$, the equator, pole, and the global and mean annual mean surface temperatures are 96K, 46K, and 90K, respectively. We found that the temperature at the high latitudes is significantly affected by the internal heating, especially during the winter solstice, suggesting that measurements of high latitude surface temperatures can be used to constrain the internal heating. We also estimate the incoming solar radiation to Enceladus, the moon of Saturn.

In ∼1990 a new source of deep water formation in the Eastern Mediterranean was found in the southern part of the Aegean sea. Till then, the only source of deep water formation in the Eastern Mediterranean was in the Adriatic sea; the rate of the deep water formation of the new Aegean source is 1 Sv, three times larger than the Adriatic source. We develop a simple three-box model to study the stability of the thermohaline circulation of the Eastern Mediterranean sea. The three boxes represent the Adriatic sea, Aegean sea, and the Ionian seas. The boxes exchange heat and salinity and may be described by a set of nonlinear differential equations. We analyze these equations and find that the system may have one, two, or four stable flux states. We conjecture that the change in the deep water formation in the Eastern Mediterranean sea is attributed to a switch between the different states on the thermohaline circulation; this switch may result from decreased temperature and/or increased salinity over the Aegean sea.

Between ~750 to 635 million years ago, during the Neoproterozoic era, the Earth experienced at least two significant, possibly global, glaciations, termed “Snowball Earth”. While many studies have focused on the dynamics and the role of the atmosphere and ice flow over the ocean in these events, only a few have investigated the related associated ocean circulation, and no study has examined the ocean circulation under a thick (~1 km deep) sea-ice cover, driven by geothermal heat flux. Here, we use a thick sea-ice flow model coupled to an ocean general circulation model to study the ocean circulation under Snowball Earth conditions. We first investigate the ocean circulation under simplified zonal symmetry assumption and find (i) strong equatorial zonal jets, and (ii) a strong meridional overturning cell, limited to an area very close to the equator. We derive an analytic approximation for the latitude-depth ocean dynamics and find that the extent of the meridional overturning circulation cell only depends on the horizontal eddy viscosity and β (the change of the Coriolis parameter with latitude). The analytic approximation closely reproduces the numerical results. Three-dimensional ocean simulations, with reconstructed Neoproterozoic continents configuration, confirm the zonally symmetric dynamics, and show additional boundary currents and strong upwelling and downwelling near the continents.

Geological evidence suggests that marine ice extended to the Equator at least twice during the Neoproterozoic era (about 750 to 635 million years ago)1, 2, inspiring the Snowball Earth hypothesis that the Earth was globally ice-covered3, 4. In a possible Snowball Earth climate, ocean circulation and mixing processes would have set the melting and freezing rates that determine ice thickness5, 6, would have influenced the survival of photosynthetic life4, 5, 7, 8, 9, and may provide important constraints for the interpretation of geochemical and sedimentological observations4, 10. Here we show that in a Snowball Earth, the ocean would have been well mixed and characterized by a dynamic circulation11, with vigorous equatorial meridional overturning circulation, zonal equatorial jets, a well developed eddy field, strong coastal upwelling and convective mixing. This is in contrast to the sluggish ocean often expected in a Snowball Earth scenario3 owing to the insulation of the ocean from atmospheric forcing by the thick ice cover. As a result of vigorous convective mixing, the ocean temperature, salinity and density were either uniform in the vertical direction or weakly stratified in a few locations. Our results are based on a model that couples ice flow and ocean circulation, and is driven by a weak geothermal heat flux under a global ice cover about a kilometre thick. Compared with the modern ocean, the Snowball Earth ocean had far larger vertical mixing rates, and comparable horizontal mixing by ocean eddies. The strong circulation and coastal upwelling resulted in melting rates near continents as much as ten times larger than previously estimated6, 7. Although we cannot resolve the debate over the existence of global ice cover10, 12, 13, we discuss the implications for the nutrient supply of photosynthetic activity and for banded iron formations. Our insights and constraints on ocean dynamics may help resolve the Snowball Earth controversy when combined with future

Geological evidence suggests that marine ice extended to the Equator at least twice during the Neoproterozoic era (about 750 to 635 million years ago)1, 2, inspiring the Snowball Earth hypothesis that the Earth was globally ice-covered3, 4. In a possible Snowball Earth climate, ocean circulation and mixing processes would have set the melting and freezing rates that determine ice thickness5, 6, would have influenced the survival of photosynthetic life4, 5, 7, 8, 9, and may provide important constraints for the interpretation of geochemical and sedimentological observations4, 10. Here we show that in a Snowball Earth, the ocean would have been well mixed and characterized by a dynamic circulation11, with vigorous equatorial meridional overturning circulation, zonal equatorial jets, a well developed eddy field, strong coastal upwelling and convective mixing. This is in contrast to the sluggish ocean often expected in a Snowball Earth scenario3 owing to the insulation of the ocean from atmospheric forcing by the thick ice cover. As a result of vigorous convective mixing, the ocean temperature, salinity and density were either uniform in the vertical direction or weakly stratified in a few locations. Our results are based on a model that couples ice flow and ocean circulation, and is driven by a weak geothermal heat flux under a global ice cover about a kilometre thick. Compared with the modern ocean, the Snowball Earth ocean had far larger vertical mixing rates, and comparable horizontal mixing by ocean eddies. The strong circulation and coastal upwelling resulted in melting rates near continents as much as ten times larger than previously estimated6, 7. Although we cannot resolve the debate over the existence of global ice cover10, 12, 13, we discuss the implications for the nutrient supply of photosynthetic activity and for banded iron formations. Our insights and constraints on ocean dynamics may help resolve the Snowball Earth controversy when combined with future