To understand non-linear water wave theories and perturbation methods. 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.
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What you'll learn
l Perturbation methods
l Stokes wave theory and solutions
l Nonlinear shallow water equations
l Boussinesq equations
l kdV equation and solitary wave solution
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
Prerequisites
It is recommended to take a previous lecture, Water Surface Waves: Small Amplitude Waves, before this lecture.
