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A freely cooling granular gas in a gravitational field undergoes a collapse to a multicontact state in a finite time. Previous theoretical [D. Volfson et al., Phys. Rev. E 73, 061305 (2006)] and experimental work [R. Son et al., Phys. Rev. E 78, 041302 (2008)] have obtained contradictory results about the rate of energy loss before the gravitational collapse. Here we use a molecular dynamics simulation in an attempt to recreate the experimental and theoretical results to resolve the discrepancy. We are able to nearly match the experimental results, and find that to reproduce the power law predicted in the theory we need a nearly elastic system with a constant coefficient of restitution greater than 0.993. For the more realistic velocity-dependent coefficient of restitution, there does not appear to be a power-law decay and the transition from granular gas to granular solid is smooth, making it difficult to define a time of collapse.
The ice sheets of the Amundsen Sea Embayment (ASE) are vulnerable to the marine ice sheet instability (MISI), which could cause irreversible collapse and raise sea levels by over a meter. The uncertain timing and scale of this collapse depend on the complex interaction between ice, ocean, and bedrock dynamics. The mantle beneath the ASE is likely less viscous (∼10 18 Pa s) than the Earth's average mantle (∼10 21 Pa s). Here we show that an effective equilibrium between Pine Island Glacier's retreat and the response of a weak viscoelastic mantle can reduce ice mass lost by almost 30% over 150 years. Other components of solid Earth response-purely elastic deformations and geoid perturbations-provide less stability than the viscoelastic response alone. Uncertainties in mantle rheology, topography, and basal melt affect how much stability we expect, if any. Our study indicates the importance of considering viscoelastic uplift during the rapid retreat associated with MISI.Plain Language Summary Portions of the West Antarctic Ice Sheet are vulnerable to an instability that could lead to rapid ice sheet collapse, significantly raising sea levels, but the timing and rates of collapse are highly uncertain. In response to such a large-scale loss of overlying ice, viscoelastically deforming mantle material uplifts the surface, alleviating some drivers of unstable ice sheet retreat. While previous studies have focused on the effects mantle deformation has on continental ice dynamics over centuries to millennia, recent seismic observations suggest that the mantle beneath West Antarctica is hot and weak, potentially affecting local glacial dynamics over timescales as short as decades. To measure the importance of viscoelastic uplift in stabilizing grounding line retreat, we coupled a high-resolution ice flow model to a viscoelastically deforming mantle. We find that rapid viscoelastic uplift can reduce the total volume of ice lost over 150 years by 30%, or 18 mm of equivalent sea level rise, making it an essential process to consider when using models to project the future evolution of marine-based ice retreat.
SUMMARY The viscoelastic load Love numbers encapsulate the Earth’s rheology in a remarkably efficient fashion. When multiplied by a sudden increment of spherical harmonic load change, they give the horizontal and vertical surface displacements and gravity change at all later times. Incremental glacial load changes thus need only be harmonically decomposed, multiplied by the Love numbers and summed to predict the Earth’s response to glacial load redistributions. The computation of viscoelastic Love numbers from the elastic, viscous and adiabatic profiles of the Earth is thus the foundation upon which many glacial isostatic adjustment models are based. Usually, viscoelastic Love numbers are computed using the Laplace transform method, employing the correspondence principle to convert the viscoelastic equations of motion into the elastic equations with complex material parameters. This method works well for a fully non-adiabatic Earth, but can accommodate realistic partially adiabatic and fully adiabatic conditions only by changing the Earth’s density profile. An alternative method of Love number computation developed by Cathles (1975) avoids this dilemma by separating the elastic and viscous equations of motion. The separation neglects a small solid-elastic/fluid-elastic transition for compressible deformation, but allows freely defining adiabatic, partially adiabatic or fully non-adiabatic profiles in the mantle without changing the Earth’s density profile. Here, we update and fully describe this method and show that it produces Love numbers closely similar to those computed for fully non-adiabatic earth models computed by the correspondence principle, finite element and other methods. The time-domain method produces Love numbers as good as those produced by other methods and can also realistically accommodate any degree of mantle adiabaticity. All method implementations are available open source.
The ice load configuration of the Barents Sea Ice Sheet (BSIS) over the last glacial cycle is in dispute. The traditional reconstruction, motivated by the observation that paleo‐shoreline emergence increases towards the center of the Barents Sea, places a single dome in the center of the Barents Sea at the Last Glacial Maximum (LGM) that collapses to island‐centered loads during deglaciation. Observations that suggest that ice flowed from the islands into the Barents even at the LGM motivate another reconstruction that places the ice loads over the islands with minimal marine ice. We analyze an ensemble of ice loads that are consistent with the geophysical observations and show that current relative sea level, GPS and gravity measurements do not and cannot distinguish a central dome from an island‐centered BSIS. What is needed are constraints in the central Barents. Improving the gravity data sufficiently will be difficult. However, obtaining even a single GPS uplift rate measurement in the central Barents would resolve the central dome versus island‐centered BSIS geometry question. Uncertainty in the Barents Sea ice load geometry provides a good illustration of statistical methods that we believe will be useful in other areas of glaciology.
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