Past Mathematical Geoscience Seminar

2 June 2017
14:15
Keaton Burns
Abstract

Dedalus is a new open-source framework for solving general partial differential equations using spectral methods.  It is designed for maximum extensibility and incorporates features such as symbolic equation entry, custom domain construction, and automatic MPI parallelization.  I will briefly describe key algorithmic features of the code, including our sparse formulation and support for general tensor calculus in curvilinear domains.  I will then show examples of the code’s capabilities with various applications to astrophysical and geophysical fluid dynamics, including a compressible flow benchmark against a finite volume code, and direct numerical simulations of turbulent glacial melting

  • Mathematical Geoscience Seminar
19 May 2017
14:15
Pippa Whitehouse
Abstract

In my research I model three components of the Earth system: the ice sheets, the ocean, and the solid Earth. In the first half of this talk I will describe the traditional approach that is used to model the impact of ice sheet growth and decay on global sea-level change and solid Earth deformation. I will then go on to explain how collaboration across the fields of glaciology, geodynamics and seismology is providing exciting new insight into feedbacks between ice dynamics and solid Earth deformation.

  • Mathematical Geoscience Seminar
5 May 2017
14:15
David Rees Jones
Abstract

In July 2011, the observation of a massive phytoplankton bloom underneath a sea ice–covered region of the Chukchi Sea shifted the scientific consensus that regions of the Arctic Ocean covered by sea ice were inhospitable to photosynthetic life. Although the impact of widespread phytoplankton blooms under sea ice on Arctic Ocean ecology and carbon fixation is potentially marked, the prevalence of these events in the modern Arctic and in the recent past is, to date, unknown. We investigate the timing, frequency, and evolution of these events over the past 30 years. Although sea ice strongly attenuates solar radiation, it has thinned significantly over the past 30 years. The thinner summertime Arctic sea ice is increasingly covered in melt ponds, which permit more light penetration than bare or snow-covered ice. We develop a simple mathematical model to investigate these physical mechanisms. Our model results indicate that the recent thinning of Arctic sea ice is the main cause of a marked increase in the prevalence of light conditions conducive to sub-ice blooms. We find that as little as 20 years ago, the conditions required for sub-ice blooms may have been uncommon, but their frequency has increased to the point that nearly 30% of the ice-covered Arctic Ocean in July permits sub-ice blooms. Recent climate change may have markedly altered the ecology of the Arctic Ocean.

  • Mathematical Geoscience Seminar
24 February 2017
14:15
Ian Hewitt
Abstract

Many northern hemisphere climate records show a series of rapid climate changes - Dansgaard-Oesgher (D-O) cycles - that recurred on centennial to millennial timescales throughout most of the last glacial period.  They consist of sudden warming jumps of order 10°C, followed generally by a slow cooling lasting a few centuries, and then a rapid temperature drop into a cold period of similar length.  Most explanations for D-O events call on changes in the strength of the Atlantic meridional overturning circulation (AMOC), but the mechanism for triggering and pacing such changes is uncertain. Changes in freshwater delivery to the ocean are assumed to be important. 

Here, we investigate whether the proposed AMOC changes could have occurred as part of a natural relaxation oscillation, in which runoff from the northern hemisphere ice sheets varies in response to each warming and cooling event, and in turn provides the freshwater delivery that controls the ocean circulation.  In this mechanism the changes are buffered and paced by slow changes in salnity of the Arctic ocean.  We construct a simple model to investigate whether the timescales and magnitudes make this a viable mechanism.  

  • Mathematical Geoscience Seminar
27 January 2017
14:15
Colin Meyer
Abstract

Radar data from both Greenland and Antarctica show folds and other disruptions to the stratigraphy of the deep ice. The mechanisms by which stratigraphy deforms are related to the interplay between ice flow and topography. Here we show that when ice flows across valleys or overdeepenings, viscous overturnings called Moffatt eddies can develop. At the base of a subglacial valley, the shear on the valley walls is transfered through the ice, forcing the ice to overturn. To understand the formation of these eddies, we numerically solve the non-Newtonian Stokes equations with a Glen's law rheology to determine the critical valley angle for the eddies to form. The decrease in ice viscosity with shear enhances shear localization and, therefore, Moffatt eddies form in smaller valley angles (steeper slopes) than in a fluid that does not localize shear, such as a Newtonian fluid. When temperature is incorporated into the ice rheology, the warmer basal ice is less viscous and eddies form in larger valley angles (shallower slopes) than in isothermal ice. We apply our simulations to the Gamburtsev Subglacial Mountains and solve for the ice flow over radar-determined topography. These simulations show Moffatt eddies on the order of 100 meters tall in the deep subglacial valleys.

  • Mathematical Geoscience Seminar
2 December 2016
14:15
Abstract

The mathematical design of the table flood demonstrator Wetropolis will be presented. Wetropolis illustrates the concepts of extreme rainfall and flooding.

It shows how extreme rainfall events  can cause flooding of a city due to groundwater and river flood peaks. Rainfall is supplied randomly in space using four outcomes (in a reservoir, on a moor, at both places or nowhere) and randomly in time using four rainfall intensities (1s, 2s, 4s, or 9s during a 10s Wetropolis day), including one extreme event, via two skew-symmetric discrete probability distributions visualised by two Galton boards. Wetropolis can be used for both public outreach and as scientific testing environment for flood mitigation and data assimilation.

More information: https://www.facebook.com/resurging.flows

  • Mathematical Geoscience Seminar
18 November 2016
14:15
Abstract

The spreading of a viscous fluid in between a rigid, horizontal substrate and an overlying elastic sheet is presented as a simplified model of the hydraulic fracturing process. In particular, the talk will focus on the case of a permeable substrate for which leak-off arrests the propagation of the fluid and permits the development of a steady state. The different regimes of  gravitationally-driven and elastically-driven flow will be explored, as will the cases of a stiff and flexible sheet, before a discussion of the influence that particles included in the fluid have on the fracture propagation. 

  • Mathematical Geoscience Seminar
4 November 2016
14:15
Abstract

Strombolian volcanoes are thought to maintain their semi-permanent eruptive style by means of counter-current two-phase convective flow in the volcanic conduit leading from the magma chamber, driven by the buoyancy provided by exsolution of volatiles such as water vapour and carbon dioxide in the upwelling magma, due to pressure release. A model of bubbly two-phase flow is presented to describe this, but it is found that the solution breaks down before the vent at the surface is reached. We propose that the mathematical breakdown of the solution is associated with the physical breakdown of the two-phase flow regime from a bubbly flow to a churn-turbulent flow. We provide a second two-phase flow model to describe this regime, and we show that the solution can be realistically continued to the vent. The model is also in keeping with observations of eruptive style.

  • Mathematical Geoscience Seminar

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