Mathematical modelling of turbidity currents

Thesis

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?'.

Authors: Fay, GL

• Publication date: 2012
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: turbidity currents; density currents; fluid mechanics; mathematical geoscience; gravity currents
• Subjects: Geophysics (mathematics); Mathematics; Fluid mechanics (mathematics)