Water Surface Waves: Finite-amplitude waves

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.

Week 1. Introduction to perturbation method

Week 2. Stokes wave theory

Week 3. Nonlinear shallow-water equations

Week 4. Boussinesq equations and KdV equation