An experimental and theoretical study of the dynamics of grounding lines

AbstractWe present an experimental and theoretical study of a thin, viscous fluid layer that flows radially under gravity from a point source into a denser inviscid fluid layer of uniform depth above a rigid horizontal surface. Near the source, the viscous layer lies in full contact with the surface, forming a vertical-shear-dominated viscous gravity current. At a certain distance from the source, the layer detaches from the surface to form a floating current whose dynamics are controlled by the viscous stresses due to longitudinal extension. We describe the dynamics of the grounded and floating components using distinct thin-layer theories. Separating the grounded and floating regions is the freely moving line of detachment, or grounding line, whose evolution we model by balancing the horizontal forces between the two regions. Using numerical and asymptotic analysis, we calculate the evolution of the system from a self-similar form at early times towards a steady state at late times. We use our solutions to illustrate how three-dimensional stresses within marine ice sheets, such as that of West Antarctica, can lead to stabilization of the grounding line. To assess the validity of the assumptions underlying our model, we compare its predictions with data from a series of laboratory experiments.This work was supported by the Engineering and Physical Sciences Research Council.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2013.26

Dynamics of laterally confined marine ice sheets

We present an experimental and theoretical study of the dynamics of laterally confined marine ice sheets in the natural limit in which the long, narrow channel into which they flow is wider than the depth of the ice. A marine ice sheet comprises a grounded ice sheet in contact with bedrock that floats away from the bedrock at a ‘grounding line’ to form a floating ice shelf. We model the grounded ice sheet as a viscous gravity current resisted dominantly by vertical shear stresses owing to the no-slip boundary condition applied at the bedrock. We model the ice shelf as a floating viscous current resisted dominantly by horizontal shear stresses owing to no-slip boundary conditions applied at the sidewalls of the channel. The two shear-dominated regions are coupled by jump conditions relating force and fluid flux across a short transition region downstream of the grounding line. We find that the influence of the stresses within the transition region becomes negligible at long times and we model the transition region as a singular interface across which the ice thickness and mass flux can be discontinuous. The confined shelf buttresses the sheet, causing the grounding line to advance more than it would otherwise. In the case that the sheet flows on a base of uniform slope, we find asymptotically that the grounding line advances indefinitely as $t^{1/3}$, where $t$ is time. This contrasts with the two-dimensional counterpart, for which the shelf provides no buttressing and the grounding line reaches a steady state (Robison, J. Fluid Mech., vol. 648, 2010, pp. 363–380).We would like to thank Dr M. Hallworth for valuable help with running the experiments and the technicians of the DAMTP G. K. Batchelor Laboratory for help with the set-up of the experimental apparatus. K.N.K. is supported by a NERC PhD studentship. The experimental data are available as supplementary material.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.3

Suppression of marine ice sheet instability

A long-standing open question in glaciology concerns the propensity for ice sheets that lie predominantly submerged in the ocean (marine ice sheets) to destabilise under buoyancy. This paper addresses the processes by which a buoyancy-driven mechanism for the retreat and ultimate collapse of such ice sheets – the marine ice sheet instability – is suppressed by lateral stresses acting on its floating component (the ice shelf). The key results are to demonstrate the transition between a mode of stable (easily reversible) retreat along a stable steady-state branch created by ice-shelf buttressing to tipped (almost irreversible) retreat across a critical parametric threshold. The conditions for triggering tipped retreat can be controlled by the calving position and other properties of the ice-shelf profile and can be largely independent of basal stress, in contrast to principles established from studies of unbuttressed grounding-line dynamics. The stability and recovery conditions introduced by lateral stresses are analysed by developing a method of constructing grounding-line stability (bifurcation) diagrams, which provide a rapid assessment of the steady-state positions, their natures and the conditions for secondary grounding, giving clear visualisations of global stabilisation conditions. A further result is to reveal the possibility of a third structural component of a marine ice sheet that lies intermediate to the fully grounded and floating components. The region forms an extended grounding area in which the ice sheet lies very close to flotation, and there is no clearly distinguished grounding line. The formation of this region generates an upsurge in buttressing that provides the most feasible mechanism for reversal of a tipped grounding line. The results of this paper provide conceptual insight into the phenomena controlling the stability of the West Antarctic Ice Sheet, the collapse of which has the potential to dominate future contributions to global sea-level rise

Fluid Transport in Geological Reservoirs with Background Flow

This paper presents fundamental analysis of the injection and release of fluid into porous media or geological reservoirs saturated by a different fluid undergoing a background flow, and tests the predictions using analogue laboratory experiments. The study reveals new results important for an understanding of the transport of hazardous contaminants through aquifers and the long-term fate of carbon dioxide ( ) in geological sequestration. Using numerical and asymptotic analysis, we describe a variety of flow regimes that arise, and demonstrate an almost instantaneous control of injected fluid by the far field conditions in geological reservoirs. For a continuous input, the flow develops a horizontal interface between the injected and ambient fluids. The background flow thereby effectively caps the height of the injected fluid into a shallower region of vertical confinement. For a released parcel of fluid, gravitational spreading is found to become negligible after a short time. A dominant control of the interface by the background pressure gradient arises, and stems from the different velocities at which it drives the injected and ambient fluids individually. Similarity solutions describing these dynamics show that the parcel approaches a slender triangular profile that grows horizontally as , where is time, a rate faster than relaxation under gravity. Shock layers develop at the front or back of the parcel, depending on whether it is more or less viscous than the ambient fluid. New analytical results describing the long-term effects of residual trapping due to capillary retention are developed, which yield explicit predictions for the time and length scales on which a parcel of becomes retained. We end by applying our results to geological contexts, concluding that even slight background motion can have considerable implications for long-term transport through the subsurface

Rapid heat discharge during deep-sea eruptions generates megaplumes and disperses tephra

Deep-marine volcanism drives Earth’s most energetic transfers of heat and mass between the crust and the oceans. While magmatic activity on the seafloor has been correlated with the occurrence of colossal enigmatic plumes of hydrothermal fluid known as megaplumes, little is known of the primary source and intensity of the energy release associated with seafloor volcanism. As a result, the specific origin of megaplumes remains ambiguous. By developing a mathematical model for the dispersal of submarine tephras, we show that the transport of pyroclasts requires an energy discharge that is sufficiently powerful (~1-2 TW) to form a hydrothermal plume with characteristics matching those of observed megaplumes in a matter of hours. Our results thereby directly link megaplume creation, active magma extrusion, and tephra dispersal. The energy flux at the plume source required to drive the dispersal is difficult to attain by purely volcanogenic means, and likely requires an additional input of heat, potentially from rapid evacuations of hot hydrothermal fluids triggered by dyke intrusion. In view of the ubiquity of submarine tephra deposits, our results demonstrate that intervals of rapid hydrothermal discharge are likely commonplace during deep-ocean volcanism

The convective Stefan problem: shaping under natural convection

What is the shape formed by a body that is melting or dissolving into an ambient fluid? We present a theoretical analysis of the dynamics of melting or dissolving bodies in the common situation where the transfer of heat or solute at the surface creates a thin thermal or solutal convective boundary layer along its surface. By conducting a general analysis of a mathematical model describing the shape evolution of such bodies (Pegler & Davies Wykes, J. Fluid Mech., vol. 900, 2020, A35), we reveal new phenomena relating to the emergence of fundamental similarity solutions, asymptotic transitions, tip structure and the conditions for the development of sharp versus blunted tips. A universal regime diagram is developed showing asymptotic transitions between two different classes of similarity solutions. With t time, the tip of initially rectangular bodies is found to descend as t4/3 at early times, but transitions to the considerable faster power of t4 at long times, for example. Surprisingly, the tips of certain shapes, including initially rectangular bodies, sharpen continuously, whilst those of others, including initially conic bodies, blunt for all times. For the former case, the tip curvature grows rapidly as t12, forming a needle-like shape. More general initial shapes can produce multiple transitions between sharpening and blunting. These results provide foundational understanding of buoyancy-driven fluid sculpting that underlies numerous natural and industrial applications

Shaping of melting and dissolving solids under natural convection

How quickly does an ice cube melt or a lump of sugar dissolve? We address the open problem of the shapes of solids left to melt or dissolve in an ambient fluid driven by stable natural convection. The theory forms a convective form of a Stefan problem in which the evolution is controlled by a two-way coupling between the shape of the body and stable convection along its surface. We develop a new model describing the evolution of such bodies in two-dimensional or axisymmetric geometries and analyse it using a combination of numerical and analytical methods. Different initial conditions are found to lead to different fundamental shapes and descent rates. For the cases of initially linear surfaces (wedges or cones), the model admits similarity solutions in which the tip descends from its initial position as t4/5 , where t is time. It is determined that the evolving shape always forms a parabola sufficiently near the tip. For steeply inclined bodies, we establish a general two-tiered asymptotic structure comprising a broad 4/3 -power intermediate near-tip region connected to a deeper parabolic region at the finest scale. The model results apply universally for any given relationship between density, viscosity, diffusivity and concentration, including two-component convection. New laboratory experiments involving the dissolution of cones of sugar candy in water are found to collapse systematically onto our theoretically predicted shapes and descent rates with no adjustable parameters

Ice fabrics in two-dimensional flows: beyond pure and simple shear

Ice fabrics – the distribution of crystal orientations in a polycrystal – are key for understanding and predicting ice flow dynamics. Despite their importance, the characteristics and evolution of fabrics produced outside of the deformation regimes of pure and simple shear flow has largely been neglected, yet they are a common occurrence within ice sheets. Here, we use a recently developed numerical model (SpecCAF) to classify all fabrics produced over a continuous spectrum of incompressible two-dimensional deformation regimes and temperatures. The model has been shown to accurately predict ice fabrics produced in experiments, where the ice has been deformed in either uniaxial compression or simple shear. Here we use the model to reveal fabrics produced in regimes intermediate to pure and simple shear, as well as those that are more rotational than simple shear. We find that intermediate deformation regimes between pure and simple shear result in a smooth transition between a fabric characterised by a girdle and a secondary cluster pattern. Highly rotational deformation regimes are revealed to produce a weak girdle fabric. Furthermore, we provide regime diagrams to help constrain deformation conditions of measured ice fabrics. We also obtain predictions for the strain scales over which fabric evolution takes place at any given temperature. The use of our model in large-scale ice flow models and for interpreting fabrics observed in ice cores and seismic anisotropy provides new tools supporting the community in predicting and interpreting ice flow in a changing climate

The dynamics of confined extensional flows

I present a theoretical and experimental study of floating viscous fluid films introduced into a channel of finite length, motivated by the flow of glacial ice shelves. The dynamics are characterized by a mixture of viscous extensional stresses, transverse shear stresses and a driving buoyancy force. A theory based on a width-integrated model is developed and investigated using analytical, asymptotic and numerical methods. With fluid introduced at a constant rate, the flow is found to approach a steady state with two possible asymptotic forms depending on the length of the channel. For channel lengths less than half the width, the flow is similar to a purely extensional one-dimensional flow, characterized by concave surface profiles and being insensitive to the position of the channel exit (or calving front). Greater lengths result in a more complex asymptotic structure in which the flow adjusts over a short distance towards a prevailing flow of universal dimensionless form. In complete contrast to the extensional regime, the prevailing flow is controlled by the position of the channel exit. Data from a new laboratory experiment involving particle velocimetry of a floating fluid film compares well with the predicted along-channel velocity. Motivated by glaciological application, the analysis is generalized to power-law rheologies and the results used to classify the flow regimes of a selection of ice shelves. The prediction for the frontal speed is in good agreement with geophysical data, indicating that the universal profile predicted by the theory is common in nature

Shaping of melting and dissolving solids under natural convection

How quickly does an ice cube melt or a lump of sugar dissolve? We address the open problem of the shapes of solids left to melt or dissolve in an ambient fluid driven by stable natural convection. The theory forms a convective form of a Stefan problem in which the evolution is controlled by a two-way coupling between the shape of the body and stable convection along its surface. We develop a new model describing the evolution of such bodies in two-dimensional or axisymmetric geometries and analyse it using a combination of numerical and analytical methods. Different initial conditions are found to lead to different fundamental shapes and descent rates. For the cases of initially linear surfaces (wedges or cones), the model admits similarity solutions in which the tip descends from its initial position as, where t is time. It is determined that the evolving shape always forms a parabola sufficiently near the tip. For steeply inclined bodies, we establish a general two-tiered asymptotic structure comprising a broad -power intermediate near-tip region connected to a deeper parabolic region at the finest scale. The model results apply universally for any given relationship between density, viscosity, diffusivity and concentration, including two-component convection. New laboratory experiments involving the dissolution of cones of sugar candy in water are found to collapse systematically onto our theoretically predicted shapes and descent rates with no adjustable parameters