Water waves in the presence of sub-surface shear: developing an experiment
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The planning and analysis of a laboratory set-up for examining the behaviour of water waves in the presence of sub-surface shear is presented in the following work. Water waves propagate on shear currents in many important applications in engineering and oceanography, and in the presence of a sub-surface shear current the properties of the wave pattern can drastically be changed. The effects of wave-current interaction are what is planned to be qualitatively and quantitatively observed in the laboratory. In the first part an introduction to the fundamental theory of water waves is presented for the still water case and for the case of a uniform current with and without shear. Additionally, the theory of ring waves and ship waves on a uniform shear current on finite depth is given. The experimental set-up in the laboratory is described, as well as measurements and experiments that have been conducted on the set-up. Different lighting and photography methods have been investigated through trial-and-error experiments, and capturing images of the wave patterns is found to be challenging as the water surface reflects light. Using two angled light sources to illuminate the flow while photographing from above proved to give better results than other approaches. Photographing the flow area using a polarization filter gave somewhat unclear visualization as the filter did not rid the surface of all reflections, and additional reflections were seen to appear when photographing at an angle compared to the results from frontal photography. Parameters in the laboratory are measured, as well as measurements of ship wake angles from different pressure source sizes. The results are seen to be significantly larger than Kelvin's angle, as according to theory. Furthermore, a set-up to perform laser Doppler velocimetry (LDV) measurements from above the free surface was made, and the velocity profile at one location of the rig was measured. The results showed that the velocity profile is parabolic. Observations and measurements lead to the conclusion that the experimental rig should be run at large water volumes and low pump settings to achieve somewhat tidy flow conditions, although improvements of the rig are needed to obtain even conditions. Some recommendations are discussed in the final chapter.