Identifier

etd-07042011-003953

Degree

Master of Science in Engineering Science (MSES)

Department

Engineering Science (Interdepartmental Program)

Document Type

Thesis

Abstract

This study focuses on solving the evolution equations for triad interaction in shallow water waves. First, the evolution equations based on Boussinesq-type equations with Pad¨¦ approximant of the exact linear phase velocity using multi-scale perturbation analysis are derived. Next, methods of solving the complex equation directly, splitting the complex function into amplitude and phase functions, and splitting complex function into real and imaginary parts are implemented to solve the evolution equations. Then the fourth-order Runge-Kutta (RK4) numerical scheme is employed to solve the evolution equations, and corresponding numerical results of three wave interaction are presented demonstrating the sensitivity of the model to the perturbation parameter ¦Å. When ¦Å=0.45, the model produces the optimal result in good agreement with the exact solution in terms of beat length as well as amplitude. The method of manufactured solutions (MMS) is utilized to verify the codes, ensuring that they have been coded correctly and are fulfilled with the capability to solve the equations.

Date

2011

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Chen, Q. Jim

DOI

10.31390/gradschool_theses.2084

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