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Title: Mathematical modelling of turbidity currents
Author: Fay, Gemma Louise
ISNI:       0000 0004 2738 7997
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2012
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Turbidity currents are one of the primary means of transport of sediment in the ocean. They are fast-moving, destructive fluid flows which are able to entrain sediment from the seabed and accelerate downslope in a process known as `ignition'. In this thesis, we investigate one particular model for turbidity currents; the `Parker model' of Parker, Pantin and Fukushima (1986), which models the current as a continuous sediment stream and consists of four equations for the depth, velocity, sediment concentration and turbulent kinetic energy of the flow. We propose two reduced forms of the model; a one-equation velocity model and a two-equation shallow-water model. Both these models give an insight into the dynamics of a turbidity current propagating downstream and we find the slope profile to be particularly influential. Regions of supercritical and subcritical flow are identified and the model is solved through a combination of asymptotic approximations and numerical solutions. We next consider the dynamics of the four-equation model, which provides a particular focus on Parker's turbulent kinetic energy equation. This equation is found to fail catastrophically and predict complex-valued solutions when the sediment-induced stratification of the current becomes large. We propose a new `transition' model for turbulent kinetic energy which features a switch from an erosional, turbulent regime to a depositional, stably stratified regime. Finally, the transition model is solved for a series of case studies and a numerical parameter study is conducted in an attempt to answer the question `when does a turbidity current become extinct?'.
Supervisor: Fowler, Andrew Cadle ; Howell, Peter D. Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Fluid mechanics (mathematics) ; Geophysics (mathematics) ; fluid mechanics ; turbidity currents ; mathematical geoscience ; gravity currents ; density currents