Title page for ETD etd-07042011-003953


Type of Document Master's Thesis
Author Zhang, Qian
Author's Email Address zhangqian06@gmail.com
URN etd-07042011-003953
Title Solving Evolution Equations for Triad Interaction of Shallow Water Waves
Degree Master of Science in Engineering Science (M.S.E.S.)
Department Engineering Science (Interdepartmental Program)
Advisory Committee
Advisor Name Title
Chen, Q. Jim Committee Chair
Tsai, Frank Committee Member
Wan, Xiaoliang Committee Member
Keywords
  • shallow water waves
  • nonlinear triad interaction
  • evolution equations
Date of Defense 2011-06-21
Availability unrestricted
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 . When =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.
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