The dynamics of miscible viscous fingering from onset to shutdown

We examine the full ‘life cycle’ of miscible viscous fingering from onset to shutdown with the aid of high-resolution numerical simulations. We study the injection of one fluid into a planar two-dimensional porous medium containing another, more viscous fluid. We find that the dynamics are distinguished by three regimes: an early-time linearly unstable regime, an intermediate-time nonlinear regime and a late-time single-finger exchange-flow regime. In the first regime, the flow can be linearly unstable to perturbations that grow exponentially. We identify, using linear stability theory and numerical simulations, a critical Péclet number below which the flow remains stable for all times. In the second regime, the flow is dominated by the nonlinear coalescence of fingers which form a mixing zone in which we observe that the convective mixing rate, characterized by a convective Nusselt number, exhibits power-law growth. In this second regime we derive a model for the transversely averaged concentration which shows good agreement with our numerical experiments and extends previous empirical models. Finally, we identify a new final exchange-flow regime in which a pair of counter-propagating diffusive fingers slow exponentially. We derive an analytic solution for this single-finger state which agrees well with numerical simulations. We demonstrate that the flow always evolves to this regime, irrespective of the viscosity ratio and Péclet number, in contrast to previous suggestions

Shear dilation of subglacial till results in time-dependent sliding laws

The dynamics of glacial sliding over water-saturated tills are poorly constrained and difficult to capture realistically in large-scale models. Experiments characterize till as a plastic material with a pressure-dependent yield stress, but the subglacial water pressure may fluctuate on annual to daily timescales, leading to transient adjustment of the till. We construct a continuum two-phase model of coupled fluid and solid deformation, describing the movement of water through the pore space of a till that is itself dilating and deforming. By forcing the model with time-dependent effective pressure at the ice-till interface, we infer the resulting relationships between basal traction, solid fraction and rate of deformation. We find that shear dilation introduces internal pressure variations and transient dilatant strengthening emerges, leading to hysteretic behaviour in low-permeability materials. The result is a time-dependent effective sliding law, with permeability-dependent lag between changes in effective pressure and the slidingspeed. This deviation from traditional steady-state sliding laws may play an important role in a wide range of transient ice-sheet phenomena, from glacier surges to the tidal response of ice streams

The influence of a poroelastic till on rapid subglacial flooding and cavity formation

We develop a model of the rapid propagation of water at the contact between elastic glacial ice and a poroelastic subglacial till, motivated by observations of the rapid drainage of supraglacial lakes in Greenland. By treating the ice as an elastic bending beam, the fluid dynamics of contact with the subglacial hydrological network, which is modelled as a saturated poroelastic till, can be examined in detail. The model describes the formation and dynamics of an axisymmetric subglacial cavity, and the spread of pore pressure, in response to injection of fluid. A combination of numerical simulation and asymptotic analysis is used to describe these dynamics for both a rigid and a deformable porous till, and for both laminar and turbulent fluid flow. For constant injection rates and laminar flow, the cavity is isostatic and its spread is controlled by bending of the ice and suction of pore water in the vicinity of the ice–till contact. For a deformable till, this control can be modified: generically, a flexural wave that is initially trapped in advance of the contact point relaxes over time by diffusion of pore pressure ahead of the cavity. While the dynamics are found to be relatively insensitive to the properties of the subglacial till during injection with a constant flux, significant dependence on the till properties is manifest during the subsequent spread of a constant volume. A simple hybrid turbulent–laminar model is presented to account for fast injection rates of water: in this case, self-similar turbulent propagation can initially control the spread of the cavity, but there is a transition to laminar control in the vicinity of the ice–till contact point as the flow slows. Finally, the model results are compared with recent geophysical observations of the rapid drainage of supraglacial lakes in Greenland; the comparison provides qualitative agreement and raises suggestions for future quantitative comparison.</jats:p

Tidal Grounding-Line Migration Modulated by Subglacial Hydrology

We present a mathematical model of the hydrology of grounding-line migration on tidal timescales, in which the ice acts elastically, overlying a connected hydrological network, with the ocean tides modelled by an oscillating far-field fluid height. The upstream grounding-line migration is driven by a fluid pressure gradient through the grounding zone, while the downstream migration is limited by fluid drainage through the till. The two processes are described using separate travelling-wave solutions, based on a model of fluid flow under an elastic sheet. The asymmetry between the up- and downstream motion allows the grounding line to act as a non-linear filter on the tidal forcing as the pressure signal propagates upstream, and this frequency modulation is discussed in the context of velocity data from ice streams across Antarctica to provide a novel constraint on till permeability

Stable and unstable miscible displacements in layered porous media

The effect of permeability heterogeneities and viscosity variations on miscible displacement processes in porous media is examined using high-resolution numerical simulations and reduced theoretical modelling. The planar injection of one fluid into a fluid-saturated, two-dimensional porous medium with a permeability that varies perpendicular to the flow direction is studied. Three cases are considered, in which the injected fluid is equally viscous, more viscous or less viscous than the ambient fluid. In general it is found that the flow in each case evolves through three regimes. At early times, the flow exhibits the concentration evolves diffusively, independent of both the permeability structure and the viscosity ratio. At intermediate times, the flow exhibits different dynamics including channelling and fingering, depending on whether the injected fluid is more or less viscous than the ambient fluid, and depending on the relative magnitude of the viscosity and permeability variations. Finally, at late times, the flow becomes independent of the viscosity ratio and dominated by shear-enhanced (Taylor) dispersion. For each of the regimes identified above, we develop reduced-order models for the evolution of the transversely averaged concentration and compare them to the full numerical simulations

A shallow approximation for ice streams sliding over strong beds

Ice streams are regions of rapid ice sheet flow characterised by a high degree of sliding over a deforming bed. The shallow shelf approximation (SSA) provides a convenient way to obtain closed-form approximations of the velocity and flux in a rapidly sliding ice stream when the basal drag is much less than the driving stress. However, the validity of the SSA approximation breaks down when the magnitude of the basal drag increases. Here we find a more accurate expression for the velocity and flux in this transitional regime before vertical deformation fully dominates, in agreement with numerical results. The closed-form expressions we derive can be incorporated into wider modelling efforts to yield a better characterisation of ice stream dynamics, and inform the use of the SSA in large-scale simulations

Airway tissue engineering for congenital laryngotracheal disease

Regenerative medicine offers hope of a sustainable solution for severe airway disease by the creation of functional, immunocompatible organ replacements. When considering fetuses and newborns, there is a specific spectrum of airway pathologies that could benefit from cell therapy and tissue engineering applications. While hypoplastic lungs associated with congenital diaphragmatic hernia (CDH) could benefit from cellular based treatments aimed at ameliorating lung function, patients with upper airway obstruction could take advantage from a de novo tissue engineering approach. Moreover, the international acceptance of the EXIT procedure as a means of securing the precarious neonatal airway, together with the advent of fetal surgery as a method of heading off postnatal co-morbidities, offers the revolutionary possibility of extending the clinical indication for tissue-engineered airway transplantation to infants affected by diverse severe congenital laryngotracheal malformations. This article outlines the necessary basic components for regenerative medicine solutions in this potential clinical niche

Bridging the gap between high and low performing pupils through performance learning online analysis and curricula

Metacognition is a neglected area of investment in formal education and in teachers’ professional development. This paper presents an approach and tools, created by a London-based company called Performance Learning Education (PL), for supporting front-line teachers and learners in developing metacognitive competencies. An iterative process adopted by PL in developing and validating its approach is presented, demonstrating its value to real educational practices, it’s research potential in the area of metacognition, and its AI readiness, especially in relation to modelling learners’ non-cognitive competencies

Maternal race-ethnicity, immigrant status, country of birth, and the odds of a child with autism spectrum disorder

The risk of autism spectrum disorder varies by maternal race–ethnicity, immigration status, and birth region. In this retrospective cohort study, Western Australian state registries and a study population of 134 204 mothers enabled us to examine the odds of autism spectrum disorder with intellectual disability in children born from 1994 to 2005 by the aforementioned characteristics. We adjusted for maternal age, parity, socioeconomic status, and birth year. Indigenous women were 50% less likely to have a child with autism spectrum disorder with intellectual disability than Caucasian, nonimmigrant women. Overall, immigrant women were 40% less likely to have a child with autism spectrum disorder with intellectual disability than nonimmigrant women. However, Black women from East Africa had more than 3.5 times the odds of autism spectrum disorder with intellectual disability in their children than Caucasian nonimmigrant women. Research is implicated on risk and protective factors for autism spectrum disorder with intellectual disability in the children of immigrant women