Hankin, Barry Gwyn
(1995)
*Modelling the Dispersion of a Passive Tracer in Complex Open Channel Flows Using Random Walk, Particle Tracking Techniques.*
PhD thesis, Lancaster University.

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## Abstract

A random walk, particle tracking model is used to study the dispersion characteristics of passive tracers in three different turbulent shear flows of varying geometric and hydrodynamic complexity. The first half of the thesis is concerned with the application of random walk models to observations of two flows in the Flood Channel Facility at Hydraulics Research, Wallingford (an in-bank, 100mm flow depth and an over-bank, 176mm flow depth). A sensitivity analysis was undertaken in which several different random walk models were applied to the data. These were based on different inferences about the Lagrangian fluctuating velocity field. The different random walk models were used, since the actual form of the Lagrangian velocity statistics for an inhomogeneous flow is not known. The random walk models were semi-empirically fitted to the data, such that the macroscale particle distributions were in close agreement with the observed tracer concentration distributions, at a single measurement cross-section. The calibrated random walk models were then used to predict the statistics of the evolving tracer concentration distribution further downstream. It was found that at both the calibration and prediction stages, random walk models based on different perturbations, were able to match the observed concentration distributions to within the estimated experimental uncertainties. This property will hereinafter be referred to as equifinality. In the second half of this thesis, a random walk, streamtube-based particle tracking model is used to study the dispersion characteristics of the flow in a meander bend of an upland gravel-bed river. A fieldwork campaign was undertaken in which measurements of velocity, turbulence statistics and rhodamine tracer mass-flux distributions from a dye-tracer experiment, were collected. These measurements were analysed and used to calibrate the random walk model using the same technique as for the channel flows. It was again found that the model could be calibrated such that the particle distributions matched the observed relative tracer mass flux distributions to within the estimated uncertainties.