Past 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
8 May 2015
14:15
Abstract
Alternating, fast cloud level zonal winds on Jupiter have been accurately measured for several decades but their depth of penetration into the Jovian interior, which is closely associated with the origin of the winds, still remains highly controversial. The Juno spacecraft, now on its way to Jupiter and will arrive there in 2016, will probe the depth of penetration of the zonal winds by accurately measuring their effects on the high-order zonal gravitational coefficients at unprecedentedly high precision. Interpretation of these gravitational measurements requires an accurate description of the shape, density structure and internal wind profile. We shall discuss the mathematical theory and accurate numerical simulation for the gravitational field of rapidly rotating, non-spherical gaseous Jupiter.
  • Mathematical Geoscience Seminar
22 April 2015
14:00
Lucas Goehring
Abstract
Contraction cracks form captivating patterns such as those seen in dried mud or the polygonal networks that cover the polar regions of Earth and Mars. These patterns can be controlled, for example in the artistic craquelure sometimes found in pottery glazes. More practically, a growing zoo of patterns, including parallel arrays of cracks, spiral cracks, wavy cracks, lenticular or en-passant cracks, etc., are known from simple experiments in thin films – essentially drying paint – and are finding application in surfaces with engineered properties. Through such work we are also learning how natural crack patterns can be interpreted, for example in the use of dried blood droplets for medical or forensic diagnosis, or to understand how scales develop on the heads of crocodiles. I will discuss mud cracks, how they form, and their use as a simple laboratory analogue system. For flat mud layers I will show how sequential crack formation leads to a rectilinear crack network, with cracks meeting each other at roughly 90°. By allowing cracks to repeatedly form and heal, I will describe how this pattern evolves into a hexagonal pattern. This is the origin of several striking real-world systems: columnar joints in starch and lava; cracks in gypsum-cemented sand; and the polygonal terrain in permafrost. Finally, I will turn to look at crack patterns over uneven substrates, such as paint over the grain of wood, or on geophysical scales involving buried craters, and identify when crack patterns are expected to be dominated by what lies beneath them. In exploring all these different situations I will highlight the role of energy release in selecting the crack patterns that are seen.
  • Mathematical Geoscience Seminar
13 March 2015
14:15
Abstract
Ice streams are narrow bands of rapidly sliding ice within an otherwise slowly flowing continental ice sheet. Unlike the rest of the ice sheet, which flows as a typical viscous gravity current, ice streams experience weak friction at their base and behave more like viscous 'free films' or membranes. The reason for the weak friction is the presence of liquid water at high pressure at the base of the ice; the water is in turn generated as a result of dissipation of heat by the flow of the ice stream. I will explain briefly how this positive feedback can explain the observed (or inferred, as the time scales are rather long) oscillatory behaviour of ice streams as a relaxation oscillation. A key parameter in simple models for such ice stream 'surges' is the width of an ice stream. Relatively little is understood about what controls how the width of an ice stream evolves in time. I will focus on this problem for most of the talk, showing how intense heat dissipation in the margins of an ice stream combined with large heat fluxes associated with a switch in thermal boundary conditions may control the rate at which the margin of an ice stream migrates. The relevant mathematics involves a somewhat non-standard contact problem, in which a scalar parameter must be chosen to control the location of the contact region. I will demonstrate how the problem can be solved using the Wiener-Hopf method, and show recent extensions of this work to more realistic physics using a finite element discretization.
  • Mathematical Geoscience Seminar

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