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SNUx: Water Surface Waves: Finite-amplitude waves

To understand non-linear water wave theories and perturbation methods

Water Surface Waves: Finite-amplitude waves
4 weeks
1–2 hours per week
Self-paced
Progress at your own speed
This course is archived

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
  • Video Transcript: English
  • Associated skills:Waves (Electronics)

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

Who can take this course?

Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.

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