Nonlinear resonance of trapped waves on a plane beach

Linear edge waves were first found mathematically by Stokes (1846). It has long been a topic of interest, since edge waves are believed to be responsible for the formation of beach cusps. Galvin (1965) was the first to observe in the laboratory that edge wave mode of frequency w can be excited by incident waves of frequency w. Guza and Bowen (1976) gave a theoretical explanation of the nonlinear mechanism of sub-harmonic resonance. This type of theory has been extended by Minzoni & Whitham (1977), Rockliff (1978), and Rockliff & Smith (1985), among others. Rockliff also initiated a. theory whereby subharmonic resonance can be achieved by an incident wave of frequency w, which leads to second harmonic at the second order to excite the edge wave. Their theory was however incomplete. The goal of this thesis is to extend the existing theories in order to show other paths to resonance. The nearshore region is a plane beach of small slope. For all cases we shall derive the evolution equations governing the edge wave amplitudes and analyze the stability of the equilibrium (static or dynamic) state. We first study in Chapter 2 synchronous resonance as a special case. We shall show that interaction between the edge wave and the incident/reflected wave also generates circulation cells on the beach.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Li, Guangda, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Chiang C. Mei.

• Civil and Environmental Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/38576
• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Identifier URI

http://dspace.mit.edu/handle/1721.1/38576

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38576