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Chapter 6
Surface gravity water waves
6.1 BASIC CONCEPTS OF WATER WAVES
This chapter covers the subject of water waves, that is, the propagation and
transformation of surface water waves driven by the gravitational force.
Gravity water waves constitute part of the free surface, unsteady (usually
periodic) class of flows. Traditionally this subject is covered under the disciplines of coastal, ocean or maritime engineering (U.S. Army Corps of
Engineers 2002; Kim 2009).
The forms of the mathematical models to be presented and numerically
solved are the simplest ones, though useful and operational. Simplifying
assumptions such as linearity, periodicity and single wave frequency will be
made in order to avoid mathematical and numerical complications. Those
assumptions, however, do not affect the intended scope and pedagogical
value of the book. One-dimensional models of wave propagation will be
presented and applied within their validity limits. The wave models will
be used to describe, even approximately, an array of interesting physical
phenomena such as wave shoaling, wave breaking, partial wave reflection,
absorption of wave energy due to friction and wave generation and propagation due to bed deformation (the phenomenon known as tsunami waves).
The models will be subsequently extended to two spatial dimensions in
order to simulate wave modulation phenomena such as wave refraction,
wave diffraction, wave breaking and so on. Understanding of those phenomena is indispensable for the design of coastal, harbour, and maritime
structures (Komen et al. 1994; Lin 2008).
In the following paragraphs, some basic definitions and notions of
water waves theory will be reviewed and summarized (Sorensen 2006).
Wavelength, L, is the distance from crest to crest (or trough to trough), c o is
the wave celerity (the speed of the propagation of the surface deformation,
not of the water particles) and T is the wave period. These three variables
are connected via the simple equation
L = c o T
(6.1)
Chapter 6
Surface gravity water waves
6.1 BASIC CONCEPTS OF WATER WAVES
This chapter covers the subject of water waves, that is, the propagation and
transformation of surface water waves driven by the gravitational force.
Gravity water waves constitute part of the free surface, unsteady (usually
periodic) class of flows. Traditionally this subject is covered under the disciplines of coastal, ocean or maritime engineering (U.S. Army Corps of
Engineers 2002; Kim 2009).
The forms of the mathematical models to be presented and numerically
solved are the simplest ones, though useful and operational. Simplifying
assumptions such as linearity, periodicity and single wave frequency will be
made in order to avoid mathematical and numerical complications. Those
assumptions, however, do not affect the intended scope and pedagogical
value of the book. One-dimensional models of wave propagation will be
presented and applied within their validity limits. The wave models will
be used to describe, even approximately, an array of interesting physical
phenomena such as wave shoaling, wave breaking, partial wave reflection,
absorption of wave energy due to friction and wave generation and propagation due to bed deformation (the phenomenon known as tsunami waves).
The models will be subsequently extended to two spatial dimensions in
order to simulate wave modulation phenomena such as wave refraction,
wave diffraction, wave breaking and so on. Understanding of those phenomena is indispensable for the design of coastal, harbour, and maritime
structures (Komen et al. 1994; Lin 2008).
In the following paragraphs, some basic definitions and notions of
water waves theory will be reviewed and summarized (Sorensen 2006).
Wavelength, L, is the distance from crest to crest (or trough to trough), c o is
the wave celerity (the speed of the propagation of the surface deformation,
not of the water particles) and T is the wave period. These three variables
are connected via the simple equation
L = c o T
(6.1)