This thesis presents an approach to predicting a 3-dimensional, 3-component\ud velocity field of a fluid \ud ow that possesses a homogeneous dimension. At the\ud core of this approach is the technique of stochastic estimation, which is commonly\ud used to combine a small number of instantaneous measurements with\ud previously acquired statistical data, to produce a prediction of the flow over\ud a large number of locations. In the proposed technique, particle image velocimetry\ud (PIV) is used to provide measurements for the stochastic estimation\ud procedure, and the statistical stationarity along the homogeneous dimension of the flow is exploited to extend the use of stochastic estimation to provide a\ud full volumetric prediction.\ud The first section concerns the prediction performance of stochastic estimation.\ud It is shown how the traditional approach to stochastic estimation is\ud equivalent to ordinary least squares (OLS) regression. The properties of OLS,\ud previously unconsidered in stochastic estimation literature, are presented, and\ud shown to have a number of practical uses in the design and implementation\ud of stochastic estimation procedures. Several alternative approaches to flow\ud prediction are selected for further study, and their performance is compared\ud in a series of trials, based on data from a numerically simulated channel flow.\ud The newly-introduced biased techniques are shown to outperform or equal the accuracy of the stochastic estimation techniques across the entire range of\ud parameters under investigation.\ud The second section introduces the proposed volumetric prediction technique.\ud A proof of concept is obtained using volumetric data from the simulated\ud channel flow, and the resulting predictions show excellent quantitative\ud and qualitative agreement with the original data. The predicted vortex ring\ud data compares favourably with previous theoretical and experimental studies,\ud and visualisation of the volumetric data appears to show the existence of\ud secondary vortical structures around the outside of the ring core, which have\ud previously only been observed in numerical simulations
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