Andrew Wells

Abstract:

Marine-terminating glaciers, such as those along the coastline of Greenland, often release meltwater into the ocean in the form of subglacial discharge plumes. Though these plumes can dramatically alter the mass loss along the front of a glacier, the conditions surrounding their genesis remain poorly constrained. In particular, little is known about the geometry of subglacial outlets and the extent to which seawater may intrude into them. Here, the latter is addressed by exploring the dynamics of an arrested salt wedge – a steady-state, two-layer flow system where salty water partially intrudes a channel carrying fresh water. Building on existing theory, we formulate a model that predicts the length of a non-entraining salt wedge as a function of the Froude number, the slope of the channel and coefficients for interfacial and wall drag. In conjunction, a series of laboratory experiments were conducted to observe a salt wedge within a rectangular channel. For experiments conducted with laminar flow (Reynolds number Re < 800), good agreement with theoretical predictions are obtained when the drag coefficients are modelled as being inversely proportional to Re. However, for fully turbulent flows on geophysical scales, these drag coefficients are expected to asymptote toward finite values. Adopting reasonable drag coefficient estimates for this flow regime, our theoretical model suggests that typical subglacial channels may permit seawater intrusions of the order of several kilometres. While crude, these results indicate that the ocean has a strong tendency to penetrate subglacial channels and potentially undercut the face of marine-terminating glaciers.

Abstract:

Arctic sea ice is one of the most sensitive components of the Earth’s climate system. The underlying ocean plays an important role in the evolution of the ice cover through its heat flux at the ice-ocean interface which moderates ice growth and melt. Despite its importance, the spatio-temporal variations of this heat flux are not well understood. In this work, we combine direct numerical simulations of turbulent convection over fractal surfaces and analysis of time-series data from the Surface Heat Budget of the Arctic Ocean (SHEBA) program using Multifractal Detrended Fluctuation Analysis (MFDFA) to understand the nature of fluctuations in this heat flux. We identify key physical processes associated with the observed Hurst exponents calculated by the MFDFA, and how these evolve over time. We also discuss ongoing work on constructing simple stochastic models of the ocean heat flux to the ice, and potential use as a parameterisation.

Abstract:

Freshwater flux from the melting of Greenland’s Ice Sheet is thought to account for 25% of the observed rise in global mean sea level between 1992 and 2011, with a significant proportion of this associated with increased freshwater flux from marine terminating glaciers within coastal fjords. It has been suggested that increased ocean temperatures have triggered the retreat of Greenland’s outlet glaciers, with the melting of submarine glacier termini leading to an acceleration of inland regions of the ice sheet. Global climate  models  currently  operate  at  resolutions  too  coarse  to resolve  ice-ocean  interaction  on  the length  scales  typical  of  coastal  fjords. Therefore, a parameterization scheme is required to incorporate the relevant physics into such models.

As a first step towards such a parameterisation scheme, we develop theoretical understanding of the first order controls on heat and freshwater exchanges in Greenland’s proglacial fjords, guided by computational simulations in MITgcm. Fjords are modelled with idealised geometries, considering cases with and without bathymetric sills. The model parameterises melting at the glacier terminus, and non-hydrostatic flow in one or more buoyant plumes that form from fresh subglacial discharge at the glacier grounding line. We systematically explore how the overturning circulation and heat transport through a fjord respond to varying subglacial discharge.

In a subglacial-discharge dominated regime with flat bathymetry, we find that the horizontally integrated vertical flow structure set by buoyant plumes at the ice face remains unmodified along the length of the fjord, and is independent of the fjord width. For cases with either single or multiple subglacial-discharge plumes, we derive scaling laws for the heat and freshwater exchanges using buoyant plume theory, finding that the water in contact with the ice face mirrors that outside the fjord. This picture is complicated in the presence of a bathymetric sill, which can inhibit the transportation of deep coastal waters into the fjord. We conclude by discussing how our scaling laws might be used as a simple parameterisation of proglacial fjord dynamics in regimes where subglacial discharge controls the flow strength. We discuss how these results might be extended to incorporate the competing effects of circulation driven by along-fjord and along-shelf winds.

Abstract:

© 2019 The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time.