This thesis considers the problem of tidal and thermal propagation of water within a shallow estuary, with specific reference to the Port River Estuary in South Australia. A system of two - dimensional laterally integrated equations are obtained from the general three - dimensional equations of continuity, momentum conservation and thermodynamics by integration over the width of the estuarial channel, and this system is further integrated over depth to obtain a set of one-dimensional equations. A numerical model is developed from these equations, using explicit finite differences to approximate the tidal equations ( continuity and motion ) and implicit differences to model the temperature equation. The model is extended to include a number of interconnecting channels, and discusses boundary conditions to determine transports, elevations and temperatu along each of the channels. Verification of the numerical model is achieved by comparing results obtained from the model with analytic solutions for similar situations. These comparisons show good agreement between the two solutions. A two - dimensional numerical model is obtained by first non - dimensionalizing the laterally integrated equations with respect to the depth coordinate, and then using explicit finite differences to solve the equations of continuity, motion and temperature. Different schemes are considered in order to provide the best means of approximating the differential equations, and these are discussed with reference to stability, convergence and efficiency. The two models are applied to the Port River Estuary, where the Torrens Island Power Station pumps heated water into one of the channels within the estuary. Tidal elevations obtained from the models compare favourably with data collected at various points in the estuary. Unfortunately, no transport or temperature measurements are available to verify the models, but results obtained from both models are consistent. The temperature results tend to suggest that recirculation of heated water from the outflow region to the point where water is drawn into the Power Station does occur at most stages of a tidal cycle. This recirculation can lower the efficiency of the power station, and possible alternatives are put forward to prevent this becoming an economical problem for the Station. / Thesis (Ph.D.)--Department of Applied Mathematics, 1976.
| Identifer | oai:union.ndltd.org:ADTP/263673 |
| Date | January 1976 |
| Creators | Teubner, Michael David |
| Source Sets | Australiasian Digital Theses Program |
| Language | en_US |
| Detected Language | English |
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