VII. Water Wave Theory
Learning Objectives
- Identify the parts of basic waves, including terminology used to describe their motion (i.e. period, frequency, speed etc.)
- Categorize wave types, including wind-driven ocean waves
- Understand fundamental equations for modeling water waves, beginning with conservation of mass, momentum, and vorticity
- Motivate the need for initial conditions and boundary conditions to complete set of governing equations
- Establish basic assumptions of rigid impermeable and interfacial boundary conditions
- Derive formulations for velocity potential and surface elevation using the assumptions of linearized small amplitude wave theory
- Understand the circular motion of water particles involved in wave motion
- Categorize wave types by shallow, intermediate, and deep water
- Explore the impacts of water depth on wave physics
- Explore of non-linear waves, including Stokes, Cnoidal, and solitary waves both visually and mathematically
Sections 1, 4, and 5 of this chapter borrow from Introduction to Oceanography by Paul Webb which is licensed under the CC BY 4.0 International License.
Will my newly designed ship hull be able to avoid capsizing in storm conditions? Can I redesign the fishing pier at my local state park to withstand waves crashing on its piles for 25 years? To what angle will my company’s offshore wind turbine tilt in hurricane conditions?
Answering these engineering questions requires a solid understanding of how to model ocean waves. Before we can model the complex dynamics of the offshore environment, a more basic understanding of water wave theory is needed. This chapter focuses largely on wind-driven surface gravity waves, the types that affect the motion and loading on engineering applications located on or near the surface of the ocean.
We’ll begin with an overview of wave definitions and types before delving into the fundamental equations of fluid motion. Solutions to the governing equations and their boundary conditions will result in a variety of wave theories, including linear and non-linear types. The differences between shallow, intermediate, and deep water waves will be delineated. Finally, we’ll establish how to select the proper wave theory for a given design scenario.
This chapter is a distillation of more detailed texts about water wave theory, the marine environment, and hydrodynamics, from the following:
- Apel, J.R. Principles of Ocean Physics. Academic Press, New York, 1987.
- Crapper, G.D. Introduction to Water Waves. Ellis Horwood Limited, New York, 1984.
- Lamb, H. Hydrodynamics. CJ Clay and Sons, Cambridge, 1895.
- Mei, C. The Applied Dynamics of Ocean Surface Waves. John Wiley and Sons, New York, 1982.
- Phillips, O.M. The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge, 1977.
- Stoker, J.J. Water Waves: The Mathematical Theory with Applications. Interscience Publishers, Inc, New York, 1957.
- Whitham, G.B. Linear and Nonlinear Waves. John Wiley and Sons, New York, 1974.
