Search for: All records

Abstract Icy satellites host topography at many length scales, from rifts and craters on the small end to equatorial‐pole shell thickness differences that are comparable to these bodies' circumference. The current paradigm is that icy satellites should not host stable small‐scale topography. This idea comes from previous work using a “shallow”‐shell model (i.e., ice shell circumference much larger than shell thickness) with a rigid outer crust. In this limit, large‐scale topography relaxes over a longer time scale than small‐scale features. Here we revisit this paradigm and analyze relaxation of topography starting from the Stokes equations for viscous fluid flow. For a shell with a viscosity that decreases exponentially with depth, we show numerically that there is a regime where the larger viscosity outer crust acts as a nearly rigid boundary. In this case, the relaxation time scale depends on the wavelength. For the largest spatial scales, however, the time scale becomes independent of wavelength and the value is set by the average shell viscosity. However, the spatial scale that this transition occurs at becomes larger as the viscosity contrast increases, limiting the applicability of the scale‐independent relaxation rate. These results for the relaxation of topography have implications for interpreting relaxed crater profiles, inferences of ice shell thickness from topography, and upcoming observations from missions to the outer solar system. 

Abstract Glaciers and ice streams flowing over sediment beds commonly have a layer of ice‐rich debris adhered to their base, known as a “frozen fringe,” but its impact on basal friction is unknown. We simulated basal slip over granular beds with a cryogenic ring shear device while ice infiltrated the bed to grow a fringe, and measured the frictional response under different effective stresses and slip speeds. Frictional resistance increased with increasing slip speed until it plateaued at the frictional strength of the till, closely resembling the regularized Coulomb slip law associated with clean ice over deformable beds. We hypothesize that this arises from deformation in a previously unidentified zone of weakly frozen sediments at the fringe's base, which is highly sensitive to temperature and stress gradients. We show how a rheologic model for ice‐rich debris coupled with the thermomechanics of fringe growth can account for the regularized Coulomb behavior. 

Abstract Flow through partially frozen pores in granular media containing ice or gas hydrate plays an essential role in diverse phenomena including methane migration and frost heave. As freezing progresses, the frozen phase grows in the pore space and constricts flow paths so that the permeability decreases. Previous works have measured the relationship between permeability and volumetric fraction of the frozen phase, and various correlations have been proposed to predict permeability change in hydrology and the oil industry. However, predictions from different formulae can differ by orders of magnitude, causing great uncertainty in modeling results. We present a floating random walk method to approximate the porous flow field and estimate the effective permeability in isotropic granular media with specified particle size distributions, without solving for the entire flow field in the pore space. In packed spherical particles, the method compares favorably with the Kozeny‐Carman formula. We further extend this method with a probabilistic interpretation of the volumetric fraction of the frozen phase, simulate the effect of freezing in irregular pores, and predict the evolution of permeability. Employing no adjustable parameters, our results can provide insight into the coupling between phase transitions and permeability change, which plays important roles in hydrate formation and dissociation, as well as in the thawing and freezing of permafrost and ice‐bed coupling beneath glaciers. 

Frost heave occurs when the ground swells during freezing conditions due to the growth of ice lenses in the subsurface. The mechanics of ice-infiltrated sediment, or frozen fringe, influences the formation and evolution of ice lenses. As the frozen fringe thickens during freezing, progressive unloading can result in dilation of the pore space and the formation of new ice lenses. Compaction can also occur as water is expelled from the pore space and freezes onto the ice lenses. We introduce a mathematical model for compaction within frozen fringe to explore how internal variability influences the fundamental characteristics of frost heave cycles. At faster freezing rates, compaction below ice lenses can generate complex dynamics and chaos when the frozen fringe follows a consolidation law based solely on the sediment yield stress. The complex oscillations arise because a downward water flux below the compacting zone generates a distributed zone of weakening. We introduce viscous effects into the compaction law through a bulk viscosity to determine how the cycles could be influenced by the creep of ice through the pore space. Localized zones of decompaction in the viscoplastic model can prevent the feedback mechanisms that cause complex oscillations in the perfectly plastic model. 

The sliding speed of glaciers depends strongly on the water pressure at the ice‐sediment interface, which is controlled by the efficiency of water transport through a subglacial hydrological system. The least efficient component of the system consists of “distributed” flow everywhere beneath the ice, whereas the “channelized” drainage through large, thermally eroded conduits is more efficient. To understand the conditions under which the subglacial network channelizes, we perform a linear stability analysis of distributed flow, considering competition between thermal erosion and viscous ice collapse. The calculated growth rate gives a stability criterion, describing the minimum subglacial meltwater flux needed for channels to form, but also indicates the tendency to generate infinitely narrow channels in existing models. We demonstrate the need to include lateral heat diffusion when modeling melt incision to resolve channel widths, which allows continuum models to recover Röthlisberger channel behavior. We also show that low numerical resolution can suppress channel formation and lead to overestimates of water pressure. Our derived channelization criterion can be used to predict the character of subglacial hydrological systems without recourse to numerical simulations, with practical implications for understanding changes in ice velocity due to changes in surface melt runoff. 

Wire regelation is a common tabletop demonstration of the pressure-dependence of the ice melting temperature where a loaded wire moves from top to bottom through a block of ice, yet leaves the block intact. With the background temperature fixed at the bulk melting point ∼0°C, the elevated ice and liquid pressures beneath the wire cause melting because of the negative Clapeyron slope, while refreezing takes place above the wire where the pressures are reduced. Regelation is a model for temperate glacier ice moving through small bedrock obstacles. Laboratory experiments demonstrate that regelation continues to occur, albeit at much slower velocities, when the fixed background ice temperature is cold enough that the wire load is insufficient to produce bulk melting, suggesting that premelting plays a central role. Here, we compile available data for wire regelation at all temperatures. We then develop a model for the subtemperate data points, where the film thickness depends on the temperature below the melting point. We find agreement between the power-law model and the laboratory data for slow regelation velocities, allowing us to characterize the dominant premelting mechanisms for different wire compositions. These results advance our understanding of the role of premelting in subtemperate glacier sliding. 

The ground thermal regime has a profound impact on geomorphological processes and has been suggested to be particularly important for weathering processes in periglacial environments. Several frost-related damage indices have hitherto been developed to link climate and frost weathering potential in bedrock, although only for individual points or grid cells. Here, we model ground temperature and frost weathering potential in steep rock walls in the Jotunheimen Mountains, southern Norway, along a two-dimensional profile line for the Younger Dryas Stadial-Preboreal transition (c. 11.5 ka), the Holocene Thermal Maximum (c. 7.5 ka), the Little Ice Age (1750), and the 2010s. We use an established heat flow model and frost-cracking index based on the ice segregation theory. A central innovation of our model treatment is the implementation of ensemble simulations using distributions of automatically mapped crack radii in a rock wall, whereas previous frost damage models considered only a single characteristic crack radius. Our results allowed for the identification of sites with enhanced frost weathering. Such sites are typically found between rock walls and retreating glaciers, as well as in areas where snow depth changes abruptly, resulting in large thermal gradients. Hence, frost weathering may be highly active during glacier retreat, enhancing the damage to rock walls during deglaciation by adding to the damage from stress release. The coldest climates of the Younger Dryas Stadial-Preboreal transition and the Little Ice Age were generally most favorable for frost cracking. Such timing compares well with the knowledge about the timing of rockfall accumulations in Norway. 

Abstract Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice. 

Abstract Small quantities of liquid water lining triple junctions in polycrystalline glacier ice form connected vein networks that enable material exchange with underlying basal environments. Diffuse debris concentrations commonly observed in ice marginal regions might be attributed to this mechanism. Following recent cryogenic ring-shear experiments, we observed emplacement along grain boundaries of loess particles several tens of microns in size. Here, we describe an idealized model of vein liquid flow to elucidate conditions favoring such particle transport. Gradients in liquid potential drive flow toward colder temperatures and lower solute concentrations, while deviations of the ice stress state from hydrostatic balance produce additional suction toward anomalously low ice pressures. Our model predicts particle entrainment following both modest warming along the basal interface resulting from anticipated natural changes in effective stress, and the interior relaxation of temperature and solute concentration imposed by our experimental protocols. Comparisons with experimental observations are encouraging, but suggest that liquid flow rates are somewhat higher and/or more effective at dragging larger particles than predicted by our idealized model with nominal parameter choices. Diffuse debris entrainment extending several meters above the glacier bed likely requires a more sophisticated treatment that incorporates effects of ice deformation or other processes. 

Ice-infiltrated sediment, or frozen fringe, is responsible for phenomena such as frost heave, ice lenses and metres of debris-rich ice under glaciers. Understanding frozen fringes is important as frost heave is responsible for damaging infrastructure at high latitudes and sediment freeze-on at the base of glaciers can modulate subglacial friction, influencing the rate of global sea level rise. Here we describe the thermomechanics of liquid water flow and freezing in ice-saturated sediments, focusing on the conditions relevant for subglacial environments. The force balance that governs the frozen fringe thickness depends on the weight of the overlying material, the thermomolecular force between ice and sediments across liquid premelted films and the water pressure required by Darcy flow. We combine this mechanical model with an enthalpy method that conserves energy across phase change interfaces on a fixed computational grid. The force balance and enthalpy model together determine the evolution of the frozen fringe thickness and our simulations predict frost heave rates and ice lens spacing. Our model accounts for premelting at ice–sediment contacts, partial ice saturation of the pore space, water flow through the fringe, the thermodynamics of the ice–water–sediment interface and vertical force balance. We explicitly account for the formation of ice lenses, regions of pure ice that cleave the fringe at the depth where the interparticle force vanishes. Our model results allow us to predict the thickness of a frozen fringe and the spacing of ice lenses in subaerial and subglacial sediments.