3. Electronic Theses and Dissertations (ETDs) - All submissions

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    Algebraic closure models applied to the two-dimensional turbulent classical far wake
    (2020) Born, Kendall
    The study of turbulence in fluids is of great importance because turbulence occurs in natural phenomena and has practical uses in industry. In this dissertation, a brief history of turbulence is presented. Particular attention is then paid to the two-dimensional turbulent classical wake and the various algebraic closure models used to complete the system of equations. The system of partial differential equations is reduced to a system of ordinary differential equations using the Lie point symmetry associated with the elementary conserved vector. When comparing with experimental results, the closure models considered consists of the constant eddy viscosity model, Prandtl’s mixing length model, and Prandtl’s improved mixing length model. The profile of the mean velocity deficit for each model is plotted on the same set of axes as the experimental profile. These profiles are compared to determine which closure model provides a better prediction of the velocity profile
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    Turbulent hydraulic fracturing described by Prandtl's mixing length
    (2016-09-19) Newman, Despina
    The problem of turbulent hydraulic fracturing is considered. Despite it being a known phenomenon, limited mathematical literature exists in this field. Prandtl’s mixing length model is utilised to describe the eddy viscosity and a mathematical model is developed for two distinct cases: turbulence where the kinematic viscosity is sufficiently small to be neglected and the case where it is not. These models allow for the examination of the fluid’s behaviour and its effect on the fracture’s evolution through time. The Lie point symmetries of both cases are obtained, and a wide range of analytical and numerical solutions are explored. Solutions of physical significance are calculated and discussed, and approximate solutions are constructed for ease of fracture estimation. The non-classical symmetries of these equations are also investigated. It was found that the incorporation of the kinematic viscosity within the modelling process was important and necessary.
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    An experimental study of flow around bed forms
    (2014-06-13) Cottino, Christian Filippo Giuseppe
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