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Over the years, rapidly varying channel flow and discontinuities in the solution of fluid mechanics problems have provided stimulation and challenge to numerical modelers. Traditional finite difference and finite element methods produce accurate but oscillatory solutions. Attempts to selectively eliminate these parasitic waves have been only partially successful in that the cost of a smoother profile was a lower accuracy solution. It is common to employ either internal and external dissipation parameters or a provision of dispersive interface. In this thesis, the problem of rapidly varying open channel flow is represented by a pair of nonlinear partial differential equations which are solved by a powerful moving finite element technique. The method developed in this research is based on the linking of a novel Lagrangian mode solution with the convenience of the Eularian grid at each time step. This second order scheme was employed in solving a variety of devised and reported open channel flow problems with near discontinuities. Comparisons with solutions obtained using the finite difference and finite element methods with Crank-Nicholson centred weightings demonstrates the quality improvements which have been achieved by this moving element scheme. The basic scheme was further generalized in both spatial and temporal dimensions. Sensitivity analysis of these generalized parameters established the grid size relaxations for a variety of problems. The moving element technique solved near discontinuous and gradually varied flow problems both in supercritical and subcritical regimes. An alternate form of Petrov-Galerkin weighting function was tested and found to give promising results. Further experimentation and testing are required before implementation. The robustness of the solution procedure is indicated by the adaptation of the model from the numerical and laboratory experiment stage to field problems. The model was successfully applied to the Teton Dam break flood and flood routing problem in the (Ontario) Grand River basin. Sensitivity analysis with very mild sloped channels with topographical features such as sudden expansions and offchannel storage suggest that the Eulerian-Lagrangian mode algorithm provides the missing link between the fluid mechanics of discontinuities and a practical tool for the modelling of rapidly varying open channel flow. Doctor of Philosophy (PhD)

In cold climates, temperatures higher than the ambient have been observed near the bottom of water lakes in the vicinity of thermal discharges. Concern has been expressed about the adverse effects of such abnormally warm water on the winter ecology of lake bottoms. It is expected that the existence of a density extremum in water at 4° C and the resulting nonlinear relation between density and temperature gives rise to densimetric flows which are markedly different from those in the linear range. This thesis presents experimental and numerical investigations that give some insight into the phenomenon of the thermal bar and the manner in which it may infIuence nearshore transport processes in the vicinity of a thermal outfalI in a cold climate. The investigations are restricted to an idealized model where the lock exchange mechanism is selected due to the fact that its behaviour is close to that expected in the prototype situation. The experimental investigation provides dramatic proof that the existence of an extremum in the density-temperature relation has a profound influence on the behaviour of densimetric flows in general and lock exchange behaviour in particular. Three zones in the vicinity of a thermal bar are clearly demonstrated viz. (i) the thermal overflow region. (ii) the thermal bar, and (iii) the thermal underflow region. The experiments provide data on the horizontal scale at which sinking takes place. A numerical model has been constructed to develop a means of modelling the behaviour of a thermal bar at the outfall of a steam electric generating station cooling water system. The numerical model employs a finite-difference scheme where the resulting algebraic finite difference equations are soIved using an alternating direction implicit method and a sparse-matrix package. The numericaI modeI has been verified by comparing it to numerical solutions of four different cases of the idealized problem of steady laminar flow in an enclosed rectangular cavity with differentially heated end walIs. Moreover, additional acceleration techniques are introduced to improve the numerical solution procedure. The numerical model is employed to solve the actual problem of simulating lock exchange flows created between two water bodies having different temperatures around the temperature of maximum density (i .e. having temperatures above and below 4° C). The general behaviour which has been observed experimentally is also confirmed numerically. The sensitivity of the associated parameters is examined. The relative extension of the thermal bar is correlated with relevant system parameters. Difficulty was experienced in obtaining numerical results for the same (high) Rayleigh numbers as were used for the physical experiments. Despite this, an encouraging degree of consistency was observed between simulated and observed behaviour. The important aspect of the study is to draw attention to the adverse effects of the sinking phenomenon (thermal bar), which may occur in the vicinity of man-made warm effluents as well as in natural bodies of water during the spring warming period. The study is significant in terms of the horizontaI scaIe at which sinking takes place, for the design of power station once-through-cooling water systems that must operate in cold climate winter conditions. Doctor of Philosophy (PhD)

The project report examines the design criteria and procedures currently used in the design of sanitary sewer systems. A review of literature concentrates on procedures for the automated design of sanitary sewer systems. From the literature review, it is concluded that the cost optimisation of a variable layout together with details of sewer sizes and vertical alignment is not practicaI. The major part of the project is the development of a program which employs dynamic programming in a multi-pass mode to optimise the cost of a branched sanitary sewer system of fixed layout. The program permits some user flexibility by allowing options for defining cost data and design criteria. Detailed documentation for operating the program is provided. A critical appraisal of the effectiveness of the algorithm and a comparison with other programs which use the dynamic programming technique is presented: A measure of the sensitivity of the optimal policy to changes in the cost structure is examined. Master of Engineering (ME)