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Disturbances to the uniform stream flow of a fluid with free surface

Holmes, Rachel (2014) Disturbances to the uniform stream flow of a fluid with free surface. PhD thesis, Murdoch University.

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We consider two main problems involving disturbances to uniform stream flow. In the first part of the thesis we examine flow over topography with particular interest in obtaining subcritical solutions with no downstream waves. Solutions to the linearised, fully nonlinear and weakly nonlinear problem are computed for two different types of topography. An array of waveless solutions corresponding to one or more trapped waves are computed at a range of different Froude numbers and are shown to provide a rather elaborate mosaic of solution curves in parameter space. The free surface is shown to evolve into different shapes as we track these waveless contours through parameter space. In addition, for one type of bottom topography, certain values of the dimensionless flow rate and obstruction height are shown to have waveless solutions for almost all obstruction separation distances greater than some particular value. In the second part of the thesis we examine the flow past a line sink. We consider the fully nonlinear problem with the inclusion of surface tension and investigate the maximum sink strength for a given stream flow, before examining non-unique solutions. The addition of surface tension allows for a more thorough investigation into the characteristics of the solutions and produces some interesting results. The breakdown of steady solutions with surface tension appears to be caused by a curvature singularity as the flow rate approaches the maximum. The non-uniqueness in solutions is shown to occur for a range of parameter values in all cases with non-zero surface tension. The work involved in this thesis has application in design of submerged structures and water quality management in reservoirs.

Publication Type: Thesis (PhD)
Murdoch Affiliation: School of Engineering and Information Technology
Supervisor: Hocking, Graeme
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