· · · Repository Hydraulic Engineering Reports

The city and harbor of Hilo, located on the northeast coast of the island of Hawaii, have been severely damaged by numerous tsunamis. Physical features which play an important role in the formation of tsunami bores at Hilo are the submarine ridge formations in deep water outside the bay mouth and the nearly vertical cliffs along the Hamalcua coast which reflect the tsunami wave into the harbor. The purpose of this paper is to discuss the Hilo Harbor Tsunami Model and this reflected wave and its effects. The tests described and the resultant information presented herein, unless otherwise noted, were obtained from research conducted under the Hilo Harbor Model Study of the United States Army Corps of Engineers by the Honolulu Engineer District. The permission granted hy the Chief of Engineers to publish this information is appreciated.

This is a presentation of recent computer results from a previously published theory of the deformation of solitary waves on a sloping beach. No attempt will be made here to review or derive the pertinent equations, and only those geometrical aspects of the theory will be introduced which are necessary for interpretation of the results. The method used here in solving Laplace's equation for the velocity potential W of the steady-state solitary wave and for its free surface determined jointly by a kinematic condition on the surface particles and by Bernoulli's equation with the pressure set equal to zero is illustrated in Fig. 1. The velocity potential is first defined inside a fixed region, the infinite strip, which will contain the solitary wave as a subdomain. Neumann conditions, are assigned to both the upper and lower boundaries of this strip of width b. Singularities producing the velocity field can be located anywhere between the free surface of the fluid and the upper edge of the strip; but, for convenience, the singularities of the trial potential function were constrained to the upper boundary.

Using a multiple-scale perturbation method we derive a set of governing equations describing the transformation of long wave and short wave components in a wave group. These equations are derived from Boussinesq equations with the assumption that the length scale of wave group modulation is in the same order of magnitude as that of the bottom variation, and is much longer than the length scale for the carrier (short) waves. Therefore the reflection of carrier waves by the topographical variation is small and neglected. Numerical examples are presented to show that long waves associated with wave group can be reflected resonantly by a field of periodic sandbars.

A least squares method to separate the incident and reflected spectra from the measured co-existing spectra is presented. This method requires a simultaneous measurement of the waves at three positions in the flume which are in reasonable proximity to each other and are on a line parallel to the direction of wave propagation. Experimental investigations have shown that there is qood agreement between the incident spectra calculated by the least squares method and the incident spectra measured concurrently in a side channel.

Background report on how to make realistic waves in laboratory flumes, including the method of splitting wave signals into incoming and reflecting waves