Tsunamis -- the propagation of long waves onto a shelf
Creators: name: Goring, Derek Garard
Publisher: name: California Institute of Technology
Year: 1978

description: The various aspects of the propagation of long waves onto a
shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf.

A numerical method of solving the one-dimensional Boussinesq
equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the dirlection of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments.

A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories.

The solution of the linear nondispersive theory for harmonic
waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented.

Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the
shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.
description: © 1978 W. M. Keck Laboratory of Hydraulics and Water Resources. California Institute of Technology. 

Several people assisted in the execution of this investigation and it is with sincere gratitude that the writer acknowledges their help here. Professor Fredric Raichlen, my thesis advisor, generously provided
guidance, encouragement and assistance in all aspects of the
project. Professor Thomas J. R. Hughes gave advice and encouragement in the development of the finite element program. Discussions with Dr. Robert C. Y. Koh were of great help in the development of many of the numerical techniques used in the analysis and data reduction. His program, MAGIC, was used extensively, especially for plotting many of the figures. Fellow student Thierry Lepelletier of ten acted as a sounding board and his advice was helpful. Mr. Elton F. Daly, supervisor of the shop and laboratory, gave invaluable assistance in  all aspects of the design, construction and maintenance of laboratory equipment which made the experimental phase of this project a pleasure. Mr. Joseph J. Fontana and Mr. Richard
Eastvedt constructed the laboratory equipment; Mr. David Byrum assisted with the experiments and drafted the figures; Mr. Peter Chang and Miss Ella Wong assisted with the experiments and with data reduction; Mrs. Adelaide R. Massengale typed the manuscript. My wife, Trish, and children, Sonia and Todd, supported and helped me with the their patience and love.

The research was supported by NSF Grant Nos. ENV72-03587 and
ENV77-20499. The New Zealand Ministry of Works and Development generously granted the writer leave on full pay with allowances for the entire period of study. Experiments were conducted at the W. M. Keck Laboratory of Hydraulics and Water Resources.
description: Submitted - KH-R-38.pdf