The frequent presence of ripples on the free surface of water. on both thin film flows and ponds or lakes motivates this theoretical investigation into the propagation of ripples on gravity waves. These ripples are treated as "slowly-varying" waves in a reference frame where the gravity wave flow is steady. The methods used are those of the averaged Lagrangian (Whitham 1965,1967,1974) and the averaged equations of motion (Phillips 1966) which are shown to be equivalent. The capillary wave modulation is taken to be steady in the reference frame which brings the gravity wave, or gravity driven flow, to rest. Firstly the motion over ponds or lakes is considered. Linear capillary-gravity waves are examined in order to set the scene. Crapper's (1957) exact finite-amplitude waves are examined next to show the actual behaviour of the flow field. The underlying gravity driven flow is that of pure gravity waves over an' "infinite" depth liquid. These gravity waves are modelled with "numerically exact" solutions for periodic plane-waves. The initial studies are inviscid and show that steep gravity waves either "absorb" or "sweep-up" a range of capillary waves or, alternatively, cause them to break in the vicinity of gravity wave crests. Improvements on the theory are made by including viscous dissipation of wave energy. This leads to a number of solutions approaching "stopping velocities" or the "stopped waves solution". In addition to these effects "higher-order dispersion" is introduced for weakly nonlinear waves near linear caustics. This clarifies aspects of the dissipation results and shows that wave reflection sometimes occurs. Secondly, waves on thin film flows are considered. Linear capillary-gravity waves are again examined in order to set the scene. Kinnersley's (1957) exact finite-amplitude waves are examined next to show the actual behaviour of the flow field. The underlying gravity driven flow is given by shallow water gravity waves. No modelling of these is necessary simply because they are included within Whitham's or Phillips' equations ab initio. This study is inviscid and shows the unexpected presence of critical velocities at which pairs of solution branches originate. iii

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There have been countless research investigations taking place on Marion Island (MI), both ecological and geological, which have reached conclusions that must necessarily neglect the impacts of wind on the systems under study. Since only the dominant wind direction of the general atmospheric wind is known from weather and satellite data, not much can be said about local wind conditions at ground level. Therefore, a baseline Computational Fluid Dynamics (CFD) model has been developed for simulating wind patterns over Marion and Prince Edward Islands, a South African territory lying in the subantarctic Indian Ocean. A review of the current state of the art of Computational Wind Engineering (CWE) revealed that large-scale Atmospheric Boundary Layer (ABL) simulations have been successfully performed before with varying degrees of success. With ANSYS Fluent chosen as the numerical solver, the Reynolds-Averaged Navier-Stokes (RANS) equations were set up to simulate a total of 16 wind flow headings approaching MI from each of the cardinal compass directions. The standard k-epsilon turbulence closure scheme with modified constants was used to numerically approximate the atmospheric turbulence. A strategy was devised for generating a reusable mesh system to simulate multiple climatic conditions and wind directions around MI. In conjunction with the computational simulations, a wind measurement campaign was executed to install 17 wind data logging stations at key locations around MI. Raw data output from the stations were cleaned and converted into an easily accessible MySQL database format using the Python scripting language. The Marion Island Recorded Experimental Dataset (MIRED) database contains all wind measurements gathered over the span of two years. The decision was taken to focus on validating only three of the 16 cardinal wind directions against the measured wind data; North-Westerly, Westerly and South-Westerly winds. An initial interrogation of the simulation results showed that island-to-island wake interactions could not be ignored as the turbulent stream from MI could definitely be intercepted by its neighbour under the right conditions, and vice versa. An underestimation of the true strength of the Coriolis effect led to larger wind deflection in the simulations than originally expected, thus resulting in the wind flow at surface levels having an entirely different heading to what was intended. The westerly and south-westerly wind validation cases did not seem too badly affected by the lapse in judgement but the north-westerly case suffered strong losses in accuracy. Significant effort was put into quantifying the error present in the simulations. After a full validation exercise, it was finally resolved to apply a conservative uncertainty factor of 35 % when using these simulations to predict actual wind speed conditions. Similarly, the predicted wind direction can only be trusted within the bounds of a 35 degree prediction uncertainty. Under these circumstances, the baseline CFD model was successfully validated against the measured wind data and can thus be used in further research. In terms of post-processing, all the wind direction simulations have been combined into a single wind velocity map, generated by weighting each of the simulations by the frequency of wind prevalence measured in the corresponding wind sector. A second turbulence intensity combined map has been provided using similar techniques. These maps, as well as the individual wind maps showing all 16 cardinal wind directions, are believed to be helpful to many future biological studies on MI as well as any possible forays into wind energy generation on the island. Despite the encountered deficiencies, this project offers significant value to academia by providing a reliable method of predicting fine-scale wind patterns in a location previously devoid of any accurate data. Furthermore, it has highlighted where future CFD attempts can be improved in order to produce a compelling approximation of the realistic atmospheric phenomena occurring in the Marion Island territory. While error cannot be avoided when modelling such complex systems, it has been well quantified and discussed here so that any further research may make informed judgements in future studies. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2021. / South African National Antarctic Programme (SANAP) grant number 110726 / National Research Foundation (NRF) / Mechanical and Aeronautical Engineering / MEng (Mechanical Engineering) / Unrestricted

This study analyzed the ability of computational fluid dynamic software to accurately predict the flow coefficient of three bottom-load ball valves to develop a design which can accurately control flow rate.