Atmospheric warming threatens to accelerate the retreat of the Antarctic Ice Sheet by increasing surface melting and facilitating 'hydrofracturing' [1][2][3][4][5][6][7] , where meltwater flows into and enlarges fractures, potentially triggering ice-shelf collapse [3][4][5][8][9][10] . The collapse of ice shelves that 'buttress' [11][12][13] the ice sheet accelerates ice flow and sea-level rise [14][15][16] . However, we do not currently know if and how much of the buttressing regions of Antarctica's ice shelves are vulnerable to hydrofracture if inundated with water. Here we provide two lines of evidence suggesting that many buttressing regions are vulnerable. First, we train a deep convolutional neural network (DCNN) to map the surface expressions of fractures in satellite imagery across all Antarctic ice shelves. Second, we develop a fracture stability diagram based on linear elastic fracture mechanics (LEFM) to predict where basal and dry surface fractures form under today's stress condition. We find close agreement between the theoretical prediction and the DCNN-mapped fractures, despite limitations associated with detecting fractures in satellite imagery. Finally, we use the LEFM theory to predict where surface fracture would become unstable if filled with water. Many regions regularly inundated with meltwater today are resilient to hydrofracturing -stresses are low enough that all water-filled fractures are stable. Conversely, 60% ±10% of ice shelves (by area) both buttress upstream ice and are vulnerable to hydrofracture if inundated with water. The DCNN-map confirms the presence of fractures in these buttressing regions. Increased surface melting 17 could trigger hydrofracturing if it leads to water inundating the widespread vulnerable regions we identify. These are regions where atmospheric warming may have the largest impact on ice-sheet mass balance.

After a bubble bursts at a liquid surface, the collapse of the cavity generates capillary waves, which focus on the axis of symmetry to produce a jet. The cavity and jet dynamics are primarily controlled by a non-dimensional number that compares capillary inertia and viscous forces, i.e. the Laplace number La= ργR0/µ 2 , where ρ, µ, γ and R0 are the liquid density, viscosity, interfacial tension, and the initial bubble radius, respectively. In this paper, we show that the time-dependent profiles of cavity collapse (t < t0) and jet formation (t > t0) both obey a |t − t0| 2/3 inviscid scaling, which results from a balance between surface tension and inertia forces. Moreover, we present a scaling law, valid above a critical Laplace number, which reconciles the time-dependent scaling with the recent scaling theory that links the Laplace number to the final jet velocity and ejected droplet size. This leads to a self-similar formula which describes the history of the jetting process, from cavity collapse to droplet formation.

SignificanceViscous fingering commonly takes place during injection of one fluid that displaces a resident fluid in a porous medium. Fingering normally is promoted where the injected fluid is less viscous than the resident fluid being displaced. We propose a design of a porous medium in the form of an ordered structure to suppress or trigger (depending on the application) viscous fingering in porous media without modifying fluid properties or wettability. We utilize pore-scale direct numerical simulations, state-of-art experiments and analysis to derive predictive tools to evaluate effects of various parameters on controlling viscous fingering in porous media. Moreover, we propose generalized analytical solutions and a phase diagram for the parameter space affecting viscous fingering patterns.

When a pressurized fluid is injected into an elastic matrix, the fluid generates a fracture that grows along a plane and forms a fluid-filled disc-like shape. We report a laboratory study of such a fluid-driven crack in a gelatin matrix, study the crack shape as a function of time and investigate the influence of different experimental parameters such as the injection flow rate, Young’s modulus of the matrix and fluid viscosity. We choose parameters so that effects of material toughness are small. We find that the crack radius R ( t ) increases with time t according to t α with α =0.48±0.04. The rescaled experimental data at long times for different parameters collapse based on scaling arguments, available in the literature, showing R ( t )∝ t 4/9 from a balance of viscous stresses from flow along the crack and elastic stresses in the surrounding matrix. Also, we measure the time evolution of the crack shape, which has not been studied before. The rescaled crack shapes collapse at longer times and show good agreement with the scaling arguments. The gelatin system provides a useful laboratory model for further studies of fluid-driven cracks, which has important applications such as hydraulic fracturing.