Wave overtopping and partial standing waves

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Umeyama, Motohiko
Ocean waves -- Analysis
thesis / dissertation description
In this study, first the surface displacement of standing waves IS derived from the finite amplitude approximation when the wave elevation exceed a breakwater with a vertical wall. Some important phenomena related to wave motion are also studied. Second, a basic concept is explained to obtain a total amount of wave overtopping, considering the property of standing waves in front of the vertical wall. Third, computer experiments are carried out In order to estimate the surface displacement of waves and the total amount of wave overtopping. These calculations are compared with the results of laboratory experiments. A perturbation method representing a non-linear gravity water waves is applied to the vertical displacement of the water surface and the velocity potential to derive a standing wave equation at wave overtopping. The author gives consideration to the solution of Goda and Abe (1968), who dealt with the standing wave as a combination of incident wave, reflective wave and bound wave (secondary effect by two waves) and calculated the surface displacement for various wave conditions. In this study this method is expanded to predict the temporal and spatial free surface displacement, the reflection effect, and the effect to the incident wave height in front of the breakwater when the crest level of the breakwater is lowered below the maximum wave elevation and the wave overtopping takes place. In addition to the non-linear treatment of the standing wave, the wave crest and trough levels and the variation of mean water level are studied to ascertain the interaction of waves and structure in non-overtopping and overtopping conditions. A theoretical investigation is conducted to study the behavior of wave overtopping in the presence of a vertical wall. A hypothesis is proposed to calculate the quantity of overtopping water during an entire wave period. The hypothesis is based on the energy equation. The total amount of wave overtopping is calculated by integrating a function of the free surface elevations of perfect and partial standing waves at the vertical wall. Experiments were performed to verify the theories in a two-dimensional wave channel where a vertical breakwater model was placed. The surface displacement of partial standing waves was measured at several points between the breakwater and 150cm from the breakwater. The surface displacements, calculated using the finite amplitude method are shown to be in agreement with test data for which the crest levels of the breakwater were chosen 4cm, and 8cm above still water level, and above maximum wave elevations. The comparison of results of the numerical method of wave overtopping with data obtained from measurements by another investigator, shows a reasonable agreement despite the simple hypothesis that was assumed.