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dc.contributor.authorConnell, Robert J.en
dc.date.accessioned2008-08-27T02:39:16Z
dc.date.issued2008en
dc.identifier.urihttps://hdl.handle.net/10182/592
dc.description.abstractThis thesis develops a one-dimensional version of a new data driven model of turbulence that uses the KL expansion to provide a spectral solution of the turbulent flow field based on analysis of Particle Image Velocimetry (PIV) turbulent data. The analysis derives a 2nd order random field over the whole flow domain that gives better turbulence properties in areas of non-uniform flow and where flow separates than the present models that are based on the Navier-Stokes Equations. These latter models need assumptions to decrease the number of calculations to enable them to run on present day computers or super-computers. These assumptions reduce the accuracy of these models. The improved flow field is gained at the expense of the model not being generic. Therefore the new data driven model can only be used for the flow situation of the data as the analysis shows that the kernel of the turbulent flow field of undular hydraulic jump could not be related to the surface waves, a key feature of the jump. The kernel developed has two parts, called the outer and inner parts. A comparison shows that the ratio of outer kernel to inner kernel primarily reflects the ratio of turbulent production to turbulent dissipation. The outer part, with a larger correlation length, reflects the larger structures of the flow that contain most of the turbulent energy production. The inner part reflects the smaller structures that contain most turbulent energy dissipation. The new data driven model can use a kernel with changing variance and/or regression coefficient over the domain, necessitating the use of both numerical and analytical methods. The model allows the use of a two-part regression coefficient kernel, the solution being the addition of the result from each part of the kernel. This research highlighted the need to assess the size of the structures calculated by the models based on the Navier-Stokes equations to validate these models. At present most studies use mean velocities and the turbulent fluctuations to validate a models performance. As the new data driven model gives better turbulence properties, it could be used in complicated flow situations, such as a rock groyne to give better assessment of the forces and pressures in the water flow resulting from turbulence fluctuations for the design of such structures. Further development to make the model usable includes; solving the numerical problem associated with the double kernel, reducing the number of modes required, obtaining a solution for the kernel of two-dimensional and three-dimensional flows, including the change in correlation length with time as presently the model gives instant realisations of the flow field and finally including third and fourth order statistics to improve the data driven model velocity field from having Gaussian distribution properties. As the third and fourth order statistics are Reynolds Number dependent this will enable the model to be applied to PIV data from physical scale models. In summary, this new data driven model is complementary to models based on the Navier-Stokes equations by providing better results in complicated design situations. Further research to develop the new model is viewed as an important step forward in the analysis of river control structures such as rock groynes that are prevalent on New Zealand Rivers protecting large cities.en
dc.language.isoenen
dc.publisherLincoln Universityen
dc.subjectdata driven modelen
dc.subjectturbulenceen
dc.subjectsurface wavesen
dc.subjectundular hydraulic jumpen
dc.subjectkernelen
dc.subjectKarhunen-Loéveen
dc.subjectProper Orthogonal Decompositionen
dc.subjectrandom flow fielden
dc.subjectregression coefficient functionen
dc.subjectcovarianceen
dc.subjectstochasticen
dc.subjectNavier-Stokes equationsen
dc.subjectKarhunen-Loéveen
dc.subject2nd orderen
dc.subjectvarianceen
dc.subjectopen channel flowen
dc.subjectsimulationen
dc.subjectrock groyneen
dc.titleUnstable equilibrium : modelling waves and turbulence in water flowen
dc.typeThesis
thesis.degree.grantorLincoln Universityen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen
dc.subject.marsdenFields of Research::290000 Engineering and Technology::290800 Civil Engineering::290802 Water and sanitary engineeringen
dc.subject.marsdenFields of Research::290000 Engineering and Technology::291100 Environmental Engineering::291101 Environmental engineering modellingen
dc.subject.marsdenFields of Research::230000 Mathematical Sciencesen
lu.contributor.unitLincoln Universityen
lu.contributor.unitLincoln Agritechen
pubs.organisational-group/LU
pubs.organisational-group/LU/Lincoln Agritech
pubs.publication-statusPublisheden


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