Coastal Engineering Journal

A verifiable predictive model for the distribution of the maximum wave from a finite number of waves in a stationary sea state has been an elusive goal. The well-known Rayleigh model overpredicts the maximum wave in a sea state. There are numerous theoretical and empirical alternatives to the Rayleigh model, but none can be identified as the model of choice. A simulation methodology is introduced to retain the essential features of the theoretical background in Gaussian random noise but to avoid further compromising assumptions in the interpretation of wave height in the amplitude domain. A probability distribution for the highest wave can be associated directly with an empirical or measured variance spectrum. Spectral shape has a definite influence on the location and width of the predicted distributions. Sharper spectral forms are associated with higher maximum waves.

Based on the linear long wave theory, analytical solutions are obtained for the propagation of tsunamis with an arbitrary incident wave profile around a conical island. The validity of the theory is verified through comparisons with two laboratory datasets. Effects of incident wave profile on the distribution of runup height and on the maximum runup height along the coastline of an island are discussed on the basis of this theory.

Based on the linear long wave theory, a theoretical solution is obtained for the transient tsunamis propagating into a conical island having a vertical wall around its coastline. The solutions are compared with the numerical solutions obtained by the Leap-Frog finite difference method using a staggered grid system to examine the relationship between the grid size and the accuracy of numerical simulation. The comparison reveals that Aida's parameter, which is a representative to evaluate the numerical error, is represented by the function of the simple parameter, . The criterion for grid size selection is determined, once the required numerical accuracy is set for the prediction of the maximum tsunami height and so on.

Based on the linear long wave theory, a theoretical solution was obtained for the tsunami, which propagated from a tsunami source generated on the shelf with a straight coastline and a uniform slope. The solution shows that the behavior of a tsunami generated on the shelf is affected by the conditions of the tsunami source. The tsunami propagation is classified into three types by examining the generated edge waves. The limit of conditions providing each propagation type is determined mainly by the source distance to the coastline. The empirical relations are derived which evaluate the characteristics of induced tsunami by using the tsunami source parameters such as the lengths of the long-axis and short-axis, the location and the direction of the tsunami source and so on. The effect of the Coriolis force is also discussed.

This study investigates the interaction of water waves with a vertical flexible membrane of a finite extent which is less than the water depth. The cases considered include that of a membrane descending from the water surface or ascending from the seabed, and that of an immersed membrane with gaps at both the top and the bottom. Linear wave theory and small membrane response are assumed and used. A numerical solution is developed based on eigenfunction expansions for the wave velocity potential and membrane motion. The computed results agree well with the reported results of a rigid barrier and of a flexible membrane spanning the entire depth. It is found that cancellation can occur from wave diffraction across the gap and that arising from the membrane motion resulting in a small transmitted wave. The membrane extent, location in the water column and tension are significant factors governing the wave interaction. The effect of these parameters, as well as wave frequency and wave incidence direction, on the transmitted wave is discussed.

An analytical model has been developed that can predict the scattering of irregular waves normally incident upon an array of vertical cylinders. To examine the predictability of the developed model, laboratory experiments have been made for the reflection and transmission of irregular waves from arrays of circular cylinders with various diameters and gap widths. Though the overall agreement between measurement and calculation is fairly good, the model tends to over- and under-predict the reflection and transmission coefficients, respectively, as the gap width decreases. The model also underestimates the energy loss coefficients for small gap widths because it neglects the evanescent waves near the cylinders. The peaks of the measured spectra of the reflected and transmitted waves slightly shift towards higher frequencies compared with that of the incident wave spectrum probably because of the generation of shorter period waves due to the interference of the cylinders. Both model and experimental data show that the wave reflection and transmission become larger and smaller, respectively, as the wave steepness increases, which is a desirable feature of the cylinder breakwaters.