On the generation of surfable ship waves, Part II: The application of stereo photo technique measuring water surface elevation and surface flow velocities

Abstract

Wave pools are designed to mimic surfing conditions as they exist along coasts. The Liquid Time Wave Pool concept, invented by Greg Webber, suggests a new method for wave generation. Waves are generated by a hull which moves in a channel. These "ship waves" break on a slope creating surf. Key feature of the concept is to make ship waves surfable. To investigate the possibility of creating surfable ship waves an experiment is conducted. During this experiment hulls are towed through a channel and the generated waves are measured using a stereo photo technique. The objectives of this study are to: 1) Investigate the possibility of making ship waves surfable; 2) Investigate the capability of the stereo photo technique to measure water surface elevation and surface velocity over a specific area. Existing theory offers the possibility to estimate wave fields using Froude depth numbers and the blocking of the channel cross section by the hull. The Froude depth number represents the ratio of the ship speed and the shallow water celerity. When Froude depth numbers and blocking values are low, hull speeds are much smaller than the shallow water celerity. The regime is called sub-critical and a dominating secondary wave field is expected. When Froude depth numbers and blocking values are high, hull speeds are high and currents around the hull can become critical. The hull speed when return currents become critical is called the limit speed. Hull speeds exceeding the limit speed account for the trans-critical regime. The trans-critical regime holds a dominating primary wave system and a negligible secondary wave system. The angle of the generated wave determines the peel angle of the surfing wave. The peel angle is the angle enclosed by the wave crest and the path of the breakpoint. Peel angles mainly determine the surfer speed. To gain insight in wave angles and surface velocities of ship waves and to verify existing ship wave theory a physical experiment is conducted. In the experiment hulls with different blocking coefficients are towed through a channel at different speeds covering the sub-critical and trans-critical regime. The wave field generated by the hull is simultaneously photographed by two distinct calibrated cameras. These stereo photos taken by the cameras are input to the stereo photo algorithm. The output of the algorithm is the water surface elevation and the surface flow velocity of the wave field. It is found that the stereo photo technique offers a great possibility to derive water surface elevations and surface flow velocities. Water surface elevations are verified using parallel measurements by wave gauges. Accuracy of the technique highly depends on camera calibration which must be improved. Limiting factors for accuracy using the technique are the pixel resolution of the images, computational power and the density of the floats. Using the stereo photo technique theory is validated. It is found that the wave field in the trans-critical regime holds strong currents. These strong currents make the trans-critical regime not suitable for surfing. The sub-critical regime holds weak currents and wave angles suit the range of the required peel angles. The Liquid Time Wave Pool design should account for towing speeds and blocking coefficients leading to the sub-critical regime.Civil Engineering and Geoscience