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

Abstract

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.

Tidal Grounding‐Line Migration Modulated by Subglacial Hydrology

“…As the ocean height rises, a hydrodynamic pressure gradient across the subglacial cavity forces ocean water into the grounding zone, driving the inland migration of the grounding line. This process is analogous to a fluid‐driven elastic peeling, or fracturing, problem (Hewitt et al, 2018; Lister et al, 2013; Tsai & Gudmundsson, 2015).…”

Seasonally evolving hydraulic transmissivity beneath Greenland supraglacial lakes

“…After injection of liquid, the fluid permeates from the blister through the porous substrate (light blue in Fig. 2b), the blister thickness decreases and the blister radius remains unchanged, which differs from the increasing R in Hewitt et al (2018) (14). Our lab experiments show that varying the permeability of the porous substrate significantly impacts the relaxation timescale in the experiments (Fig.…”

“…propagating on a water-filled porous sheet with an increasing and decreasing ℎ. In their model, water volume in the blister is constant and does not leak into the porous water sheet, resulting in a power-law decrease of blister height as a function of time (14). A comparison of the GPS uplift data with the power-law decay (14) and our exponential decay (equation 7) is shown in Supplementary Fig.…”

Viscous flow under an elastic sheet

“…Hocking 1983), or when the base has a porous upper layer of thickness and permeability through which the fluid also flows (e.g. Hewitt, Chini & Neufeld 2018). For these cases, the lubrication equation (2.4 a ) is modified to respectively, and due to the additional mobility as , these models admit travelling-wave solutions which touch down with .…”

“…Hocking 1983), or when the base has a porous upper layer of thickness b and permeability k through which the fluid also flows (e.g. Hewitt, Chini & Neufeld 2018). For these cases, the lubrication equation (2.4a) is modified to…”