arXiv subjects

Ian J. Hewitt

Publications and source records attributed to Ian J. Hewitt.

14 recordsLinked to original sources

arXiv2026

Groundwater feedbacks on ice sheets and subglacial hydrology

The dynamics of many of Antarctica's glaciers are modulated by a hydrological system at the base of the ice. Sedimentary basins beneath the ice bed contribute to the water budget in this hydrological system by discharging or taking up water. However, sedimentary basins are not included in most current models of ice dynamics, and little is known about their effect. In this paper we develop an idealised model of a glacier whose sliding is coupled to a subglacial hydrological system, which includes a sedimentary basin. We find that groundwater discharge (exfiltration) and recharge (infiltration) are controlled by the shape of the ice sheet and of the sedimentary basin, and that exfiltration promotes sliding whereas infiltration hinders it. Overall, the presence of a sedimentary basin leads to thicker and slower-flowing ice in the steady state. We also find that, when the ice sheet is undergoing retreating, groundwater exfiltration can lead to a positive feedback which accelerates this retreat. Our results shed light on the potential role and importance of Antarctic sedimentary basins, and how these might be incorporated into existing models of ice and subglacial hydrology.

physics.geo-ph↗

arXiv2025

A Unified Blister and Subglacial Hydrology Framework for Supraglacial Lake Drainage Events

Subglacial blisters form due to the rapid drainage of supraglacial lakes into grounded ice sheets, and are characterised by elastic ice uplift and transient ice-velocity anomalies. Although blister occurrence is confirmed by observations, the dynamics of blisters and their impacts on ice flow remain poorly represented in current subglacial hydrology models, as typical cavity-channel system models cannot capture short-timescale blister formation, propagation, and relaxation. Here we present a unified, self-consistent modelling framework that directly couples blister evolution with the subglacial drainage system, extending existing subglacial hydrology models to account for transient responses to rapid lake drainage events. Numerical simulations, motivated by field observations of wintertime lake drainages, reveal distinct seasonal behavior: during summer, lake drainage generates short-lived blisters that rapidly leak water into a pre-existing drainage system of efficient, channelised water pathways, whereas winter drainage results in persistent blisters that propagate slowly and serve as the primary meltwater pathway at the ice-bed interface. The dynamics of blister propagation and leakage in our model are governed by effective viscosity and a characteristic leakage length scale, which reflects the connection between the blister and the surrounding hydrological network. This unified model offers a valuable tool for investigating blister dynamics and their interplay with subglacial hydrology, facilitating the interpretation of observed surface uplift and ice-velocity variations following supraglacial lake drainage events.

physics.geo-ph↗

arXiv2024

Modelling the evolution of an ice sheet's weathering crust

The weathering crust is a layer of porous ice that can form at the surface of an ice sheet. It grows and decays in response changing weather and climate conditions, affecting the albedo, the melt rate, and the transport of meltwater across the surface. To understand this behaviour, we seek time-dependent solutions to a continuum, thermodynamic model for the porosity, temperature and thickness of the weathering crust, and the internal and surface melt rates. We find solutions using a numerical enthalpy method, presented in this study. We use idealised `switching' and sinusoidal forcings to explore the different dynamics exhibited during growth and decay, the timescales involved, and the impact of diurnal vs. annual variations. The results demonstrate qualitative agreement with observations, and provide insight into the relative importance of different surface heat fluxes during the growth and decay of the crust. The model therefore provides a useful tool for exploring the response of the weathering crust to climate change.

physics.geo-ph↗

arXiv2023

Soft matter physics of the ground beneath our feet

Inspired by presentations by the authors during a workshop organized at the Princeton Center for Theoretical Science (PCTS) in January 2022, we present a perspective on some of the outstanding questions related to the "physics of the ground beneath our feet." These identified challenges are intrinsically shared with the field of Soft Matter but also have unique aspects when the natural environment is studied.

cond-mat.soft↗

arXiv2022

Topological Data Analysis Detects Percolation Thresholds in Arctic Melt-Pond Evolution

During the summer melt period, ponds form on the surface of Arctic sea ice as it melts, with important consequences for ice evolution and marine ecology. Due to the ice-albedo feedback, these melt ponds experience uneven heat absorption, and exhibit complex patterns, which has motivated the development of modelling and data analysis to understand their particular dynamics. We provide a multiscale shape analysis using tools from computational algebraic topology, simultaneously capturing convexity, proximity, integrity, and feature size complementing existing single-scale quantification. Of particular interest in modelling the ponds is a percolation threshold at which local pond structure begins merging into macroscopic features. This percolation threshold has previously been observed using fractal dimension techniques. The signed Euclidean distance transform (SEDT) is a topological encoding of heterogeneous shape in binary images, and has been previously applied to porous media for percolation as well as other material behaviours. Here we adapt the SEDT for Arctic melt pond data to give a rich characterization and computation of shape, quantifying overall melt pond development in several complementary ways, and from which classical percolation and dimension results can be extracted. This orientation-invariant topological approach distinguishes different dynamical network models of melt pond evolution of varying complexity.

physics.data-an↗

arXiv2022

Bendocapillary Instability of Liquid in a Flexible-Walled Channel

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a `weaving' pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods, and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are always unstable to perturbations of sufficiently small wavenumber, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.

physics.flu-dyn↗

arXiv2022

On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology

Stokes variational inequalities arise in the formulation of glaciological problems involving contact. We consider the problem of a two-dimensional marine ice sheet with a grounding line, although the analysis presented here is extendable to other contact problems in glaciology, such as that of subglacial cavitation. The analysis of this problem and its discretisation is complicated by the nonlinear rheology commonly used for modelling ice, the enforcement of a friction boundary condition given by a power law, and the presence of rigid modes in the velocity space, which render the variational inequality semicoercive. In this work, we consider a mixed formulation of this variational inequality involving a Lagrange multiplier and provide an analysis of its finite element approximation. Error estimates in the presence of rigid modes are obtained by means of a specially-built projection operator onto the subspace of rigid modes and a Korn-type inequality. These proofs rely on the fact that the subspace of rigid modes is at most one-dimensional. Numerical results are reported to validate the error estimates.

math.NA↗

arXiv2022

Numerical approximation of viscous contact problems applied to glacial sliding

Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance in glaciology, where they arise in the study of grounding lines and subglacial cavities. In this work, we propose a novel numerical method for solving viscous contact problems based on a mixed formulation with Lagrange multipliers of a variational inequality involving the Stokes equation. The advection equation for evolving the geometry of the domain occupied by the fluid is then solved via a specially-built upwinding scheme, leading to a robust and accurate algorithm for viscous contact problems. We first verify the method by comparing the numerical results to analytical results obtained by a linearised method. Then, we use this numerical scheme to reconstruct friction laws for glacial sliding with cavitation. Finally, we compute the evolution of cavities from a steady state under oscillating water pressures. The results depend strongly on the location of the initial steady state along the friction law. In particular, we find that if the steady state is located on the downsloping or rate-weakening part of the friction law, the cavity evolves towards the upsloping section, indicating that the downsloping part is unstable.

math.NA↗

arXiv2022

Droplet trapping in bendotaxis caused by contact angle hysteresis

Passive droplet transport mechanisms, in which continuous external energy input is not required for motion, have received significant attention in recent years. Experimental studies of such mechanisms often ignore, or use careful treatments to minimize, contact angle hysteresis, which can impede droplet motion, or even arrest it completely. Here, we consider the effect of contact angle hysteresis on bendotaxis, a mechanism in which droplets spontaneously deform an elastic channel via capillary pressure and thereby move. Here, we seek to understand when contact angle hysteresis prevents bendotaxis. We supplement a previous mathematical model of the dynamics of bendotaxis with a simple model of contact angle hysteresis, and show that this model predicts droplet trapping when hysteresis is sufficiently strong. By identifying the equilibrium configurations adopted by these trapped droplets and assessing their linear stability, we uncover a sensitive dependence of bendotaxis on contact angle hysteresis and develop criteria to describe when droplets will be trapped.

physics.flu-dyn↗

arXiv2020

Compositional layering in Io driven by magmatic segregation and volcanism

Magmatic segregation and volcanic eruptions transport tidal heat from Io's interior to its surface. Several observed eruptions appear to be extremely high temperature ($\geq$ 1600 K), suggesting either very high degrees of melting, refractory source regions, or large amounts of viscous heating on ascent. To address this ambiguity, we develop a model that couples crust and mantle dynamics to a simple compositional system. We analyse the model to investigate chemical structure and evolution. We demonstrate that magmatic segregation and volcanic eruptions lead to differentiation of the mantle, the extent of which depends on how easily high temperature melts from the more refractory lower mantle can migrate upwards. We propose that Io's highest temperature eruptions originate from this lower mantle region, and that such eruptions act to limit the degree of compositional differentiation.

astro-ph.EP↗

arXiv2019

Wettability-independent droplet transport by \emph{Bendotaxis}

We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful means of transporting droplets in technological applications, for example in developing self-cleaning surfaces, and discuss the implications of our results for such applications.

cond-mat.soft↗

arXiv2017

Homogenized boundary conditions and resonance effects in Faraday cages

We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarisation of the incident field. In the electromagnetic case there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.

math-ph↗

arXiv2015

A Mathematical Model for Flash Sintering

A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from specified experimental conditions of fixed voltage and current, lead to thermal runaway or to stable conditions. We identify incipient thermal runaway as a necessary condition for the flash event, and hence identify the conditions under which this is likely to occur.

math.AP↗

arXiv2008

Spin Chirality in a Molecular Dysprosium Triangle: the Archetype of the Non-Collinear Ising Model

Single crystal magnetic studies combined with a theoretical analysis show that cancellation of the magnetic moments in the trinuclear Dy3+ cluster [Dy3(OH)2L3Cl(H2O)5]Cl3, resulting in a non-magnetic ground doublet, originates from the non-collinearity of the single ion easy axes of magnetization of the Dy3+ ions that lie in the plane of the triangle at 120 (deg.) one from each other. This gives rise to a peculiar chiral nature of the ground non-magnetic doublet and to slow relaxation of the magnetization with abrupt accelerations at the crossings of the discrete energy levels.

cond-mat.other↗