Tsunamis: The Response of Harbours With Sloping Boundaries to Long Wave Excitation

Abstract

The influence of sloping boundaries on long wave response of bays and harbours is studies in this work. Laboratory experiments are performed to help validate the theoretical analysis which is applicable to nonbreaking waves. A set of long wave equations in the Langrangian description is derived which includes terms to account for nonlinear, dispersive, and dissipative processes for wave propagation in two horizontal coordinates. A finite element model is developed based on these equations which is capable of treating arbitrary geometry and the runup of nonbreaking waves on a beach. An analytical harbour response model, capable of treating narrow rectangular harbours with variable bathymetry and sidewall geometry, is developed and applied to several simple geometries. The model shows that for a given harbour length and entrance width, the resonant frequencies and the response of a harbour are very dependent on the harbour sidewall geometry and bathymetry. Some of the nonlinear effects of the runup of nonbreaking waves on a plane beach are discussed. In particular, the time average of the water surface time history at a fixed spatial location is negative and the wave crests are smaller than the troughs. Nonlinear effects do not alter the runup maxima or minima and the maximum fluid acceleration occurs at the point of maximum rundown of the wave. Laboratory experiments were performed to determine the long wave response of a narrow rectangular harbour whose still water depth decreases linearly between the harbour entrance and the shoreline. Good agreement with the finite element model was obtained, including the prediction of the depression of the mean water level within the harbour. A three-dimensional application of the finite element model treats the runup of solitary waves on a coastline with variable bottom topography and a curved shoreline. The results indicate the model can predict the trapping of wave energy along a sloping coastal margin, a process of fundamental importance for predicting potential tsunami damage.

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