Past Mathematical Geoscience Seminar

12 February 2016
14:15
Abstract

In this talk I will review mathematical models used to describe the dynamics of ice sheets, and highlight some current areas of active research.  Melting of glaciers and ice sheets causes an increase in global sea level, and provides many other feedbacks on isostatic adjustment, the dynamics of the ocean, and broader climate patterns.  The rate of melting has increased in recent years, but there is still considerable uncertainty over  why this is, and whether the increase will continue.  Central to these questions is understanding the physics of how the ice intereacts with the atmosphere, the ground on which it rests, and with the ocean at its margins.  I will given an overview of the fluid mechanical problems involved and the current state of mathematical/computational modelling.  I will focus particularly on the issue of changing lubrication due to water flowing underneath the ice, and discuss how we can use models to rationalise observations of ice speed-up and slow-down.

  • Mathematical Geoscience Seminar
29 January 2016
14:15
Abstract

Humpback whales are iconic mammals at the top of the Antarctic food chain. Their large reserves of lipid-rich tissues such as blubber predispose them to accumulation of lipophilic contaminants throughout their lifetime. Changes in the volume and distribution of lipids in humpback whales, particularly during migration, could play an important role in the pharmacokinetics of lipophilic contaminants such as the organochlorine pesticide hexachlorobenzene (HCB). Previous models have examined constant feeding and nonmigratory scenarios. In the present study, the authors develop a novel heuristic model to investigate HCB dynamics in a humpback whale and its environment by coupling an ecosystem nutrient-phytoplankton-zooplankton-detritus (NPZD) model, a dynamic energy budget (DEB) model, and a physiologically based pharmacokinetic (PBPK) model. The model takes into account the seasonal feeding pattern of whales, their energy requirements, and fluctuating contaminant burdens in the supporting plankton food chain. It is applied to a male whale from weaning to maturity, spanning 20 migration and feeding cycles. The model is initialized with environmental HCB burdens similar to those measured in the Southern Ocean and predicts blubber HCB concentrations consistent with empirical concentrations observed in a southern hemisphere population of male, migrating humpback whales. 

  • Mathematical Geoscience Seminar
4 December 2015
14:15
Abstract

It has been conjectured that marine ice sheets (those that

flow into the ocean) are unconditionally unstable when the underlying

bed-slope runs uphill in the direction of flow, as is typical in many

regions underneath the West Antarctic Ice Sheet. This conjecture is

supported by theoretical studies that assume a two-dimensional flow

idealization. However, if the floating section (the ice shelf) is

subject to three-dimensional stresses from the edges of the embayments

into which they flow, as is typical of many ice shelves in Antarctica,

then the ice shelf creates a buttress that supports the ice sheet.

This allows the ice sheet to remain stable under conditions that may

otherwise result in collapse of the ice sheet. This talk presents new

theoretical and experimental results relating to the effects of

three-dimensional stresses on the flow and structure of ice shelves,

and their potential to stabilize marine ice sheets.

  • Mathematical Geoscience Seminar
20 November 2015
14:15
Abstract

There is wide interest in the oceanographic and engineering communities as to whether linear models are satisfactory for describing the largest and steepest waves in open ocean. This talk will give some background on the topic before describing some recent modelling. This concludes that non-linear physics produces only small increases in amplitude over that expected in a linear model — however, there are significant changes to the shape and structure of extreme wave-group caused by the non-linear physics.

  • Mathematical Geoscience Seminar
6 November 2015
14:15
Laura Stevens
Abstract

Across much of the ablation region of the western Greenland Ice Sheet, hydro-fracture events related to supraglacial lake drainages rapidly deliver large volumes of meltwater to the bed of the ice sheet. We investigate what triggers the rapid drainage of a large supraglacial lake using a Network Inversion Filter (NIF) to invert a dense local network of GPS observations over three summers (2011-2013). The NIF is used to determine the spatiotemporal variability in ice sheet behavior (1) prior to lake drainage, and in response to (2) vertical hydro-fracture crack propagation and closure, (3) the opening of a horizontal cavity at the ice-sheet bed that accommodates the rapid injection of melt-water, and (4) extra basal slip due to enhanced lubrication. We find that the opening and propagation of each summer’s lake-draining hydro-fracture is preceded by a local stress perturbation associated with ice sheet uplift and enhanced slip above pre-drainage background velocities. We hypothesize that these precursors are associated with the introduction of meltwater to the bed through neighboring moulin systems.

  • Mathematical Geoscience Seminar
16 October 2015
14:15
Abstract

Surface waves modify the fluid dynamics of the upper ocean not only through wave breaking but also through phase-averaged effects involving the surface-wave Stokes drift velocity. Chief among these rectified effects is the generation of a convective flow known as Langmuir circulation (or “Langmuir turbulence”). Like stress-driven turbulence in the absence of surface waves, Langmuir turbulence is characterized by streamwise-oriented quasi-coherent roll vortices and streamwise streaks associated with spanwise variations in the streamwise flow. To elucidate the fundamental differences between wave-free (shear) and wave-catalyzed (Langmuir) turbulence, two separate asymptotic theories are developed in parallel. First, a large Reynolds number analysis of the Navier–Stokes equations that describes a self-sustaining process (SSP) operative in linearly stable wall-bounded shear flows is recounted. This theory is contrasted with that emerging from an asymptotic reduction in the strong wave-forcing limit of the Craik–Leibovich (CL) equations governing Langmuir turbulence. The comparative analysis reveals important structural and dynamical differences between the SSPs in shear flows with and without surface waves and lends further support to the view that Langmuir turbulence in the upper ocean is a distinct turbulence regime. 

  • Mathematical Geoscience Seminar
9 October 2015
14:15
Abstract

Studies of thermal convection in planetary interiors have largely focused on convection above the critical Rayleigh number. However, convection in planetary mantles and crusts can also occur under subcritical conditions. Subcritical convection exhibits phenomena which do not exist above the critical Rayleigh number. One such phenomenon is spatial localization characterized by the formation of stable, spatially isolated convective cells. Spatial localization occurs in a broad range of viscosity laws including temperature-dependent viscosity and power-law viscosity and may explain formation of some surface features observed on rocky and icy bodies in the Solar System.

  • Mathematical Geoscience Seminar
5 June 2015
14:15
Shomeek Mukhopadhyay
Abstract

Shear Thickening fluids such as cornstarch and water show remarkable response under impact, which allows, for example, a person to run on the surface of the suspension. We perform constant velocity impact experiments along with imaging and particle tracking in a shear thickening fluid at velocities lower than 500 mm/s and suspension heights of a few cm. In this regime, where inertial effects are insignificant, we find that a solid-like dynamically jammed region with a propagating front is generated under impact. The suspension is able to support large stresses like a solid only when the front reaches the opposite boundary. These impact-activated fronts are generated only above a critical velocity. We construct a model by taking into account that sufficiently large stresses are generated when this solid like region spans to the opposite boundary and the work necessary to deform this solid like material dissipates the kinetic energy of the impacting object. The model shows quantitative agreement of the measured penetration depth using high speed video of a person running on cornstarch and water suspensions.

  • Mathematical Geoscience Seminar
22 May 2015
14:15
Simon Dadson
Abstract

The role of surface-water flooding in controlling fluxes of water and carbon between the land and the atmosphere is increasingly recognized in studies of the Earth system. Simultaneous advances in remote earth observation and large-scale land-surface and hydrological modeling promise improvements in our ability to understand these linkages, and suggest that improvements in prediction of river flow and inundation extents may result. Here we present an analysis of newly-available observational estimates of surface water inundation obtained through satellite Earth observation with results from simulations produced by using the Joint UK Land Environment Simulator (JULES) land-surface model operating at 0.5 degree resolution over the African continent. The model was forced with meteorological input from the WATCH Forcing Data for the period 1981-2001 and sensitivity to various model configurations and parameter settings were tested. Both the PDM and TOPMODEL sub-grid scale runoff generation schemes were tested for parameter sensitivities, with the evaluation focussing on simulated river discharge in sub-catchments of the Congo, Nile, Niger, Orange, Okavango and Zambezi rivers. It was found that whilst the water balance in each of the catchments can be simulated with acceptable accuracy, the individual responses of each river vary between model configurations so that there is no single runoff parameterization scheme or parameter values that yields optimal results across all catchments. We trace these differences to the model’s representation of sub-surface flow and make some suggestions to improve the performance of large-scale land-surface models for use in similar applications. Our findings also demonstrate links between episodes of extensive surface water flooding and large-scale climatic indices, although the pattern of correlations contains a level of spatial and temporal detail that warrants careful attention to the climatology of individual situations. These findings suggest that the use of Earth observation data together with improved models of large-scale hydrology have the potential to improve our ability to predict surface-water flooding and to develop our understanding of the role of flooding in driving components of the water and carbon cycles.

  • Mathematical Geoscience Seminar

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