143 leaves : ill., graphs ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.1980)--Dept. of Applied Mathematics, University of Adelaide, 1978

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.

Bibliography: leaves 238-247

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.

Includes bibliographical references (p.166-167)

Bibliography: leaves 238-247 / xvii, 247 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics,1991

Bibliography: leaves 363-374 / xxiii, 374 leaves : ill., maps ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1993

Natural and local anthropogenic changes in estuaries (e.g., sea-level rise, navigation channel construction and loss of wetlands) interact with each other and produce non-linear effects. There is also a growing recognition that tides in estuaries are not stationary. These factors together are changing the estuarine water level regime, however the implications for extreme water levels remain largely unknown. Changes over the past century in many estuaries, such as channel deepening and streamlining for navigation have significantly altered the hydrodynamics of long waves, often resulting in amplified tides (a ~85% increase in Wilmington, NC since 1900) and storm surge in estuaries. This research focuses on establishing analytical and numerical models that simulate a wide range of systems and flow conditions that combine multiple flood sources: astronomical tide, storm surge, and high river flow. To investigate the effects of estuarine bathymetry conditions (e.g., channel depth, convergence length), hurricane conditions (e.g., pressure and wind field), river discharge, and surge characteristics (e.g., time scale and amplitude and relative phase) on tide and storm surge propagation, I develop an idealized analytical model and two numerical models using Delft-3D. The Cape Fear River Estuary, NC (CFRE), and St Johns River Estuary, FL (SJRE) are used as case studies to investigate flood dynamics. The analytical approach has been compared and verified with idealized numerical models. I use data recovery, data analysis, and idealized numerical modeling of the CFRE to investigate the effects of bathymetric changes (e.g., dredging and channel modification) on tidal and storm surge characteristics over the past 130 years. Data analysis and modeling results suggest that long-term changes in tides can be used along with the tidal analysis tools to investigate changes in storm surge. Analysis indicate that tidal range in Wilmington, NC (Rkm 47) has doubled to 1.55m since the 1880s, while a much smaller increase of 0.07m observed close to the ocean in Southport (Rkm 6) since the 1920s. Further, model results suggest that the majority of long term changes in tides of this system have been caused by deepening the system from 7m to 15.5m due to dredging, rather than by changes in the coastal tides. Numerical modeling using idealized, parametric tropical cyclones suggests that the amplitude of the worst-case, CAT-5 storm surge has increased by 40-60% since the nineteenth century. Storm surges are meteorologically forced shallow water waves with time scales that overlap those of the tidal bands. Using data, I show that the surge wave can be decomposed into two sinusoidal waves. Therefore, I analytically model surge via a 3-constituent analytical tide model, where the third constituent is the dominant semi-diurnal tide and friction is linearized via Chebyshev polynomials. A constant discharge is considered to approximate fluvial effects The analytical model is used to study how surge amplitude, surge time scale, and surge-tide relative phase affect the spatial pattern of amplitude growth and decay, and how depth changes caused by channel deepening influence the magnitude of a storm surge. I use non-dimensional numbers to investigate how channel depth, surge time scale and amplitude, surge asymmetry, and relative timing of surge to tides alter the damping or amplification of surge along the estuary. The non-dimensional numbers suggest that increasing depth has similar effects as decreasing the drag coefficient. Similarly, larger time scale has an equivalent effect on tide and surge as increasing depth due to channel deepening. Analytical model results show that the extent of the surge amplification is dependent on the geometry of the estuary (e.g., depth and convergence length) and characteristics of the surge wave. Both models show that much of the alterations of water levels in estuaries is due to channel deepening for navigation purposes and that the largest temporal change occur for surges with a high surge to D2 amplitude ratio and a short time scale. Model results farther indicate that surge amplitude decays more slowly (larger e-folding) in a deeper channel for all surge time scales (12hr-72hr). Another main finding is that, due to nonlinear friction, the location of maximum change in surge wave moves landward as the channel is deepened. Thus, changes in flood risk due to channel deepening are likely spatially variable even within a single estuary. Next, I use the verified analytical model and numerical models to investigate the effects of river flow on surge wave propagation, and spatial and temporal variability of compound flooding along an estuary. To model the historic SJRE, I digitize nautical charts of SJRE to develop a numerical model. Both the numerical and analytical models are used to investigate the contribution of tide, surge, and river flow to the peak water level for historic and modern system configurations. Numerical modeling results for hurricane Irma (2017) show that maximum flood water levels have shifted landward over time and changed the relative importance of the various contributing factors in the SJRE. Deepening the shipping channel from 5.5m to 15m has reduced the impacts of river flow on peak water level, but increased the effects of tide and surge. Sensitivity studies also show that peak water level decreases landward for all river flow scenarios as channel depth increases. Model results show that the timing of peak river flow relative to the time of maximum surge causes very large changes in the amplitude of total water level, and in river flow effects at upstream locations for modern configuration than for the historic model. Changes in surge amplitudes can be interpreted by the non-dimensional friction number, which shows that depth (h), surge time scale (T=1/w), and convergence length-scale (Le) affect the damping/amplification of both tides and surge waves. Overall, this study demonstrates that a system scale alteration in local storm surge dynamics over the past century is likely to have occurred in many systems and should be considered for system management. The results of this research give the scientists and engineer a better understanding of tide, river flow, and surge interactions, and thereby contribute to an understanding of how to predict storm surges and help mitigate their destructive impacts. Future system design studies also need to consider long-term and changes of construction and development activities on storm surge risk in a broader context than has historically been the case.

Ocean tides worldwide have exhibited secular changes in the past century, simultaneous with a global secular rise in mean sea level (MSL). The combination of these two factors contributes to higher water levels, and may increase threats to coastal regions and populations over the next century. Equally as important as these long-term changes are the short-term fluctuations in sea levels and tidal properties. These fluctuations may interact to yield locally extreme water level events, especially when combined with storm surge. This study, presented in three parts, examines the relationships between tidal anomalies and MSL anomalies on yearly and monthly timescales, with a goal of diagnosing dynamical factors that may influence the long-term evolution of tides in the Pacific Ocean. Correlations between yearly averaged properties are denoted tidal anomaly trends (TATs), and will be used to explore interannual behavior. Correlations of monthly averaged properties are denoted seasonal tidal anomaly trends (STATs), and are used to examine seasonal behavior. Four tidal constituents are analyzed: the two largest semidiurnal (twice daily) constituents, M2 and S2, and the two largest diurnal (once daily) constituents, K1 and O1. Part I surveys TATs and STATs at 153 Pacific Ocean tide gauges, and discusses regional patterns within the entire Pacific Ocean. TATs with statistically significant relations between MSL and amplitudes (A-TATs) are seen at 89% of all gauges; 92 gauges for M2, 66 for S2, 82 for K1, and 59 for O1. TATs with statistically significant relations between tidal phase (the relative timing of high water of the tide) and MSL (P-TATs) are observed at 55 gauges for M2, 47 for S2, 42 for K1, and 61 for O1. Significant seasonal variations (STATs) are observed at about a third of all gauges, with the largest concentration in Southeast Asia. The effect of combined A-TATs was also considered. At selected stations, observed tidal sensitivity with MSL was extrapolated forward in time to the predicted sea level in 2100. Results suggest that stations with large positive combined A-TATs produce total water levels that are greater than those predicted by an increase in MSL alone, increasing the chances of high-water events. Conversely, negative correlation between sea level and tidal properties may mitigate somewhat against sea level rise; changes in total water levels in 2100 at stations with a negative combined A-TAT are less than that predicted by MSL rise alone. Climate change scenarios that take into account greater increases in MSL due to increased Antarctic ice melt show larger changes in total water levels over the same time period. Part II examines the mechanisms behind the yearly (TAT) variability in the Western Tropical Pacific Ocean. Significant amplitude TATs are found at more than half of 26 gauges for each of the two strongest tidal constituents, K1 (diurnal) and M2 (semidiurnal). For the lesser constituents analyzed (O1 and S2), significant trends are observed at ten gauges. Frictional mechanisms related to the El Nino Southern Oscillation (ENSO) are found to be important in influencing tides in the Western Pacific, as well as resonant triad interactions, a nonlinear coupling that exchanges energy between the M2, K1, and O1 tides. Both of these factors contribute to the observed tidal variability in the Solomon Sea region. Part III analyzes the seasonal behavior of tides (STATs) at twenty tide gauges in the Southeast Asian waters, which exhibit variation by 10-30% of mean tidal amplitudes. A barotropic ocean tide model that considers the seasonal effects of MSL, stratification, and geostrophic and Ekman velocity is used to explain the observed seasonal variability in tides due to variations in monsoon-influenced climate forcing, with successful results at about half of all gauges. The observed changes in tides are best explained by the influence of non-tidal velocities (geostrophic and Ekman), though the effect of changing stratification is also an important secondary causative mechanism. From the results of these surveys and investigations, it is concluded that short-term fluctuations in MSL and tidal properties at multiple time scales may be as important in determining the state of future water levels as the long-term trends. Global explanations for the observed tidal behavior have not been found in this study; however, significant regional explanations are found at the yearly time scale in the Solomon Sea, and at the seasonal time scale in Southeast Asia. It is likely that tidal sensitivity to annual and seasonal variations in MSL at other locations also are driven by locally specific processes, rather than factors with basin-wide coherence.