A method of solving the three-dimensional, incompressible turbulent boundary-layer equations was developed using a Crank-Nicholson implicit finite-difference technique, with the turbulent stress terms modeled with an eddy-viscosity model obtained from mixing length theory. The method was applied to two three-dimensional flow geometries for which experimental data exists and a comparison with this data showed excellent agreement. The complete computer program was sufficiently generalized for application to two-dimensional laminar and turbulent flows with arbitrary pressure gradients. The method was applied to several such test cases and the solutions agreed well with both theory and experiment. An analysis was presented to determine the conditions for which the finite difference equations were stable and convergent. The results of this analysis demonstrated that the equations are generally stable and convergent. However, care must be exercised when writing the finite difference approximation to the continuity equation, because certain finite difference formulations of the continuity equation can lead to an instability when the initial values for the distribution of the velocity normal to the bounding surface cannot be accurately specified. / Ph. D.

Knowledge of the detailed flow dynamics at the interior of branching corals is critical for a full understanding of nutrient uptake, mass transport, wave dissipation, and other essential processes. These physiological processes depend on the local velocity field, local concentration gradients of nutrients and waste, and the turbulent stresses developed on and above the coral surface. Though the large-scale hydrodynamics over coral reefs are well studied, the interior hydrodynamics, between the branches, remains uncharacterized due to limited optical and acoustic access to the interior. In the current thesis, a three-dimensional immersed boundary method in the large eddy simulation framework was used to compute the flow inside several branching coral colony geometries in order to study the effects of branch density and surface structure on the flow fields in the coral interiors. Two different Pocillopora colony species were studied at different Reynolds numbers. A ray-tracing algorithm was used for capturing the arbitrary branches of these complex geometries to obtain the three-dimensional flow fields within these colonies for the first time. The analysis showed the formation of vortices at the colony interior that stir the water column and thus passively enhance mass transport, compensating for the reduced mean velocity magnitude compared to the free stream value, within the densely branched Pocillopora meandrina colony. Further analysis showed that the mean streamwise velocity profile changes shape along the streamwise direction inside P. meandrina, whereas the mean velocity profile did not change shape from the front to the back for the loosely branched Pocillopora colony, Pocillopora eydouxi. Moreover, turbulent flow field quantities were computed for both these structures, and for two almost identical Montipora capitata colony geometries, one with, and one without roughness elements called verrucae. The analyses demonstrated significant differences in the mean velocity profiles, Reynolds stress, and other flow quantities with changes in colony branch density and surface structure. / Doctor of Philosophy / Coral reefs are the largest marine ecosystem, and play a critical role in protecting coastal areas against flooding and erosion. The majority of the world's corals are currently under threat from rising ocean temperatures, which disrupt the symbiotic relationship between the coral polyp and its symbiont algae causing coral bleaching. Bleaching involves processes mediated by the flow at the coral surface, but relatively little is known regarding the local flow dynamics between the branches of coral reefs. The current research seeks to characterize internal coral hydrodynamics, leading to insights about many critical physiological and other processes in corals, like drag formation, mixing, and mass or nutrient transport to and from the coral. In the current study, the influence of the coral branch density and surface structure on the resulting interbranch flow field were investigated by simulating the flow resulting from uniform oncoming ocean flow conditions using three-dimensional immersed boundary large eddy simulations. The detailed velocity and pressure fields were found throughout the interior of the colonies studied. A distinct mass transport mechanism was found inside one densely branched colony studied. For this coral, Pocillopora meandrina, the flow speed reduces substantially inside the coral because of the high branch density. But corals depend on the ocean flow to bring nutrients to the polyps on their surface. We found that P. meandrina sheds hundreds of small vortices from its branches, which stir the overlying water column, increasing the mass transport rate, and compensating almost exactly for the reduced flow in the interior. The study also included computing the flow through three other coral colony geometries, and comparisons of their mean velocity profiles and turbulent flow statistics in order to examine the impact of the colony branch density and surface structures on the resulting hydrodynamic flow field. The current investigation of coral hydrodynamics may lead to an increased understanding of coral health and physiological activity, and may help in designing effective interventions for the challenges facing corals, which could have impacts in the fields of coral restoration, coastal protection, and public policy in the United States and abroad.

Understanding the physics of mixing for two fluids is a complicated problem and has always been an interesting phenomenon to study. Surface discharge is the oldest, least expensive and simplest way of discharging industrial or domestic wastewater into rivers and estuaries. Because of the lower degree of dilution in surface discharges, critical conditions are more likely to occur. Having a better understanding of the mixing phenomenon in these cases will help to predict the environmental effects more accurately. In this study, surface discharges of jets into waterbodies with or without crossflows were investigated numerically and experimentally. Three-dimensional (3-D) Computational Fluid Dynamics (CFD) models were developed for studying the surface discharge of jets into water bodies using different turbulence models. Reynolds stress turbulence models and spatially filtered Large Eddy Simulation (LES) were used in the numerical models. The effects of inclusion of free surface water in the CFD models on the performance of the numerical model results were investigated. Numerical model results were compared with the experimental data in the literature as well as the experimental works performed in this study. Experimental works for buoyant and non-buoyant surface discharge of jets into crossflow and stagnant water were conducted in this study. A new setup was designed and built in the Civil Engineering Hydraulics Laboratory at the University of Ottawa to perform the desired experiments. Stereoscopic Particle Image Velocimetry (Stereo-PIV) was used to measure the instantaneous spatial and temporal 3-D velocity distribution on several planes of measurement downstream of the jet with the frequency of 40 Hz. Averaged 3-D velocity distribution was extracted on different planes of measurement to show the transformation of the velocity vectors from a “jet-like” to a “plume-like” flow regime. Averaged 3-D velocity distribution and streamlines illustrated the flow transformation of the surface jets. Experimental results detected the formation and evolution of vortices in the surface jet’s flow structure over the measurement zone. Additional turbulent flow characteristics such as the turbulent kinetic energy (k), turbulent kinetic energy dissipation rate (ϵ), and turbulent eddy viscosity (υt) were calculated using the measured time history of the 3-D velocity field.