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Tsunamis -- the propagation of long waves onto a shelf

Goring, Derek Garard (1978) Tsunamis -- the propagation of long waves onto a shelf. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechKHR:KH-R-38

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Abstract

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.


Item Type:Report or Paper (Technical Report)
Additional Information: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.
Group:W. M. Keck Laboratory of Hydraulics and Water Resources
Record Number:CaltechKHR:KH-R-38
Persistent URL:http://resolver.caltech.edu/CaltechKHR:KH-R-38
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:25987
Collection:CaltechKHR
Deposited By: Imported from CaltechKHR
Deposited On:20 Apr 2005
Last Modified:26 Dec 2012 13:51

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