Water Surface Waves: Finite-amplitude waves

To understand non-linear water wave theories and perturbation methods

Water Surface Waves: Finite-amplitude waves
This course is archived
Estimated 4 weeks
4–6 hours per week
Progress at your own speed

About this course

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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.

At a glance

  • Institution: SNUx
  • Subject: Engineering
  • Level: Advanced
  • Prerequisites:

    It is recommended to take a previous lecture, Water Surface Waves: Small Amplitude Waves, before this lecture.

  • Language: English

What you'll learn

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l Perturbation methods

l Stokes wave theory and solutions

l Nonlinear shallow water equations

l Boussinesq equations

l kdV equation and 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

About the instructors