This course covers fundamentals of nonlinear water waves based on perturbation methods. After reviewing basic techniques of perturbation methods, we study solutions for Stokes waves of deep water. After identifying the limitation of Stokes waves solution in shallow water, we then derive the nonlinear shallow-water equations. Finally, we explore the Boussinesq equations to account for (weak) dispersion and solve the kdV equation to obtain the solitary wave solution.
Overview
Syllabus
Week 1. Introduction to perturbation method
Week 2. Stokes wave theory
Week 3. Nonlinear shallow-water equations
Week 4. Boussinesq equations and KdV equation
Taught by
Yong Sung Park and Minjae Lee
