Part C | 27.1
598 Part C Coastal Design
has the potential to increase peak water levels during
storms [27.1], also implying that wave energy may penetrate further inshore. The engineer is left with many
different options to quantify the wave properties in the
coastal zone, from overly simple methods to impractically complex numerical tools.
Relative to many engineering disciplines, the use
of numerical coastal wave models for design is new.
Many analyses still rely on the simple linear wave methods described in the following section. The usage of
large-scale spectral wave models has become commonplace, as these models are efficient and well tested.
Currently, it is less common to go to detailed phaseresolving models in engineering practice. These models
provide a wave-by-wave resolution of the coastal dynamics, and can provide insight on a small spatial scale.
Such insight is important when trying to, for example, accurately estimate wave overtopping of a coastal
levee or wave impact loads on a structure. The following sections of this paper will outline the various
approaches, providing a brief literature review and theoretical background.
27.1 Wind Wave Modeling
There is a wide range of useful techniques for estimating wind wave properties in the nearshore; the
choice of which technique to use depends on limiting
factors such as the resources available, the precision required in the result, and the physical properties of the
waves themselves. The types of approaches discussed
in this section have both highly variable physical approximation as well as computational demand; these
two factors often have an inverse behavior. It is the purpose of the following presentation to outline the main
types of coastal modeling options, providing theoretical
background, numerical modeling schemes, and typical
applications.
27.1.1 Linear, Analytical and Semi-Empirical
Approaches
The simplest methods for estimating coastal wave
properties utilize linear potential wave theory. While
this theory is covered comprehensively in many textbooks [27.2], the most relevant equations are given
here. Additionally, this presentation will serve to establish the basic variable quantities used in coastal
hydrodynamic modeling. The free surface elevation Á
for a single frequency component is given by
Á D
H
2
cos  ;
where H is the wave height equal to twice the wave amplitude a. For one horizontal dimension and constant
depth, Â is the wave phase function given by
 D kx !t ;
where k is the wave number, x is a horizontal coordinate, ! is the angular frequency, and t is time. In
general terms, k and x can be vector quantities when
directional waves are considered. Wavenumber and angular frequency are related to other important physical
quantities
k D 2=L; ! D 2=T; f D 1=T ;
where L is the wavelength, or horizontal distance between two successive crests or troughs, T is the wave
period, and f is the wave frequency. The linear dispersion relation provides the connection between wave
frequency and wavelength
!
2
D gk tanh.kh/ ;
where g is gravity, h is the local water depth, and the
fluid is assumed inviscid. Expressions for fluid velocity
and pressure under the wave can be found in textbooks,
and will not be repeated here. Linear wave theory predicts closed, elliptical orbits of fluid particles under
waves, and, therefore, no net mass transport.
In the limited case of very shallow water, where
the ratio of water depth to wavelength approaches zero,
simplifications can be made to the full linear potential
theory discussed above. The dispersion relation reduces
to
!
2
D ghk
2
;
which yields a wave speed c of
c D
!
k
D
L
T
D
p
gh
and a horizontal fluid velocity u of
u D
H
2
p
g=h cos  :
These expressions should be applied only in the case of
a very long wave, such as for tides, tsunamis, and swell
598 Part C Coastal Design
has the potential to increase peak water levels during
storms [27.1], also implying that wave energy may penetrate further inshore. The engineer is left with many
different options to quantify the wave properties in the
coastal zone, from overly simple methods to impractically complex numerical tools.
Relative to many engineering disciplines, the use
of numerical coastal wave models for design is new.
Many analyses still rely on the simple linear wave methods described in the following section. The usage of
large-scale spectral wave models has become commonplace, as these models are efficient and well tested.
Currently, it is less common to go to detailed phaseresolving models in engineering practice. These models
provide a wave-by-wave resolution of the coastal dynamics, and can provide insight on a small spatial scale.
Such insight is important when trying to, for example, accurately estimate wave overtopping of a coastal
levee or wave impact loads on a structure. The following sections of this paper will outline the various
approaches, providing a brief literature review and theoretical background.
27.1 Wind Wave Modeling
There is a wide range of useful techniques for estimating wind wave properties in the nearshore; the
choice of which technique to use depends on limiting
factors such as the resources available, the precision required in the result, and the physical properties of the
waves themselves. The types of approaches discussed
in this section have both highly variable physical approximation as well as computational demand; these
two factors often have an inverse behavior. It is the purpose of the following presentation to outline the main
types of coastal modeling options, providing theoretical
background, numerical modeling schemes, and typical
applications.
27.1.1 Linear, Analytical and Semi-Empirical
Approaches
The simplest methods for estimating coastal wave
properties utilize linear potential wave theory. While
this theory is covered comprehensively in many textbooks [27.2], the most relevant equations are given
here. Additionally, this presentation will serve to establish the basic variable quantities used in coastal
hydrodynamic modeling. The free surface elevation Á
for a single frequency component is given by
Á D
H
2
cos  ;
where H is the wave height equal to twice the wave amplitude a. For one horizontal dimension and constant
depth, Â is the wave phase function given by
 D kx !t ;
where k is the wave number, x is a horizontal coordinate, ! is the angular frequency, and t is time. In
general terms, k and x can be vector quantities when
directional waves are considered. Wavenumber and angular frequency are related to other important physical
quantities
k D 2=L; ! D 2=T; f D 1=T ;
where L is the wavelength, or horizontal distance between two successive crests or troughs, T is the wave
period, and f is the wave frequency. The linear dispersion relation provides the connection between wave
frequency and wavelength
!
2
D gk tanh.kh/ ;
where g is gravity, h is the local water depth, and the
fluid is assumed inviscid. Expressions for fluid velocity
and pressure under the wave can be found in textbooks,
and will not be repeated here. Linear wave theory predicts closed, elliptical orbits of fluid particles under
waves, and, therefore, no net mass transport.
In the limited case of very shallow water, where
the ratio of water depth to wavelength approaches zero,
simplifications can be made to the full linear potential
theory discussed above. The dispersion relation reduces
to
!
2
D ghk
2
;
which yields a wave speed c of
c D
!
k
D
L
T
D
p
gh
and a horizontal fluid velocity u of
u D
H
2
p
g=h cos  :
These expressions should be applied only in the case of
a very long wave, such as for tides, tsunamis, and swell