Part C | 27
608 Part C Coastal Design
meant to provide a basis to compare the computational cost of the various models; this is a measure
of the effort required to determine a solution at every model grid node at every time step. It is remarked
that this table provides information relative to typical model usage, here meaning applications that might
arise in engineering practice or on an operational level.
Research-level applications push the domain sizes, resolutions, and applications well beyond the types given
below.
27.5 Conclusions
In this chapter, we have provided a cursory overview
of coastal wave modeling theory and methods. The
information contained here provides a useful starting
point for understanding the differences in the wide variety of approaches. Ultimately, the choice of model
will be governed by the resources available for the
study and the primary piece of physical information
that requires estimation. If resources are light and
a precise estimate of the wave conditions is not yet
needed, as might be the case for a preliminary scoping analysis, linear wave theory may be an acceptable
approach for coastal transformation. If accurate and
relatively large-scale wave height and period information is the goal, spectral models will most likely be
the best option, with the included level of nonlinearity and resolution controlled by the resources of the
project. For studies requiring detailed, small-scale, and
wave-resolved information, such as might be needed for
critical infrastructure, a Boussinesq or Navier–Stokes
approach is reasonable. It is reiterated that the background given here, in terms of the individual models
discussed, does not represent the wealth of numerical
modeling tools available to the international engineering community.
27.6 Nomenclature
Á free surface elevation
H wave height
a wave amplitude
 wave phase function
k wave number
! angular frequency
L wavelength
T wave period
f wave frequency
g gravity
h water depth
c wave speed
u horizontal fluid particle velocity
H o offshore wave height
K S shoaling coefficient
K R refraction coefficient
K D diffraction coefficient
˛ wave angle of incidence
F wave energy flux
N time-dependent wave action density
S external wave forcing, source/sink term in spectral
wave equations
C b bottom friction coefficient
G functional form of wave energy sink
E local wave energy density
" wave amplitude divided by water depth D a=h
wave number times water depth D kh
References
27.1
N. Lin, K. Emanuel, M. Oppenheimer, E. Vanmarcke: Physically based assessment of hurricane surge
threat under climate change, Nat. Clim. Change 2,
462–467 (2012)
27.2
R.G. Dean, R.A. Dalrymple: Water Wave Mechanics
for Engineers and Scientists (Prentice Hall, Englewood Cliffs 1984)
27.3
US Army Corps of Engineers: Coastal Engineering
Manual. Engineer Manual 1110-2-1100, http://chl.
erdc.usace.army.mil/cem (2002), in 6 volumes
27.4
B. Raubenheimer, R.T. Guza, S. Elgar: Wave transformation across the inner surf zone, J. Geophys.
Res. 101(C11), 25589–25597 (1996)
27.5
W.R. Dally, R.G. Dean, R.A. Dalrymple: Wave height
variation across beach of arbitrary profile, J. Geophys. Res. 90(C6), 11917–11927 (1985)
27.6
J.A. Battjes, J.P.F.M. Janssen: Energy loss and
set-up due to breaking of random waves,
Proc. 16th Coast. Eng. Conf. (1978) pp. 569–
587
27.7
E.B. Thornton, R.T. Guza: Transformation of wave
height distribution, J. Geophys. Res. 88, 5925–5938
(1983)
27.8
D.T. Resio: The estimation of wind-wave generation in a discrete spectral model, J. Phys. Oceanogr.
2(4), 510–525 (1981)
608 Part C Coastal Design
meant to provide a basis to compare the computational cost of the various models; this is a measure
of the effort required to determine a solution at every model grid node at every time step. It is remarked
that this table provides information relative to typical model usage, here meaning applications that might
arise in engineering practice or on an operational level.
Research-level applications push the domain sizes, resolutions, and applications well beyond the types given
below.
27.5 Conclusions
In this chapter, we have provided a cursory overview
of coastal wave modeling theory and methods. The
information contained here provides a useful starting
point for understanding the differences in the wide variety of approaches. Ultimately, the choice of model
will be governed by the resources available for the
study and the primary piece of physical information
that requires estimation. If resources are light and
a precise estimate of the wave conditions is not yet
needed, as might be the case for a preliminary scoping analysis, linear wave theory may be an acceptable
approach for coastal transformation. If accurate and
relatively large-scale wave height and period information is the goal, spectral models will most likely be
the best option, with the included level of nonlinearity and resolution controlled by the resources of the
project. For studies requiring detailed, small-scale, and
wave-resolved information, such as might be needed for
critical infrastructure, a Boussinesq or Navier–Stokes
approach is reasonable. It is reiterated that the background given here, in terms of the individual models
discussed, does not represent the wealth of numerical
modeling tools available to the international engineering community.
27.6 Nomenclature
Á free surface elevation
H wave height
a wave amplitude
 wave phase function
k wave number
! angular frequency
L wavelength
T wave period
f wave frequency
g gravity
h water depth
c wave speed
u horizontal fluid particle velocity
H o offshore wave height
K S shoaling coefficient
K R refraction coefficient
K D diffraction coefficient
˛ wave angle of incidence
F wave energy flux
N time-dependent wave action density
S external wave forcing, source/sink term in spectral
wave equations
C b bottom friction coefficient
G functional form of wave energy sink
E local wave energy density
" wave amplitude divided by water depth D a=h
wave number times water depth D kh
References
27.1
N. Lin, K. Emanuel, M. Oppenheimer, E. Vanmarcke: Physically based assessment of hurricane surge
threat under climate change, Nat. Clim. Change 2,
462–467 (2012)
27.2
R.G. Dean, R.A. Dalrymple: Water Wave Mechanics
for Engineers and Scientists (Prentice Hall, Englewood Cliffs 1984)
27.3
US Army Corps of Engineers: Coastal Engineering
Manual. Engineer Manual 1110-2-1100, http://chl.
erdc.usace.army.mil/cem (2002), in 6 volumes
27.4
B. Raubenheimer, R.T. Guza, S. Elgar: Wave transformation across the inner surf zone, J. Geophys.
Res. 101(C11), 25589–25597 (1996)
27.5
W.R. Dally, R.G. Dean, R.A. Dalrymple: Wave height
variation across beach of arbitrary profile, J. Geophys. Res. 90(C6), 11917–11927 (1985)
27.6
J.A. Battjes, J.P.F.M. Janssen: Energy loss and
set-up due to breaking of random waves,
Proc. 16th Coast. Eng. Conf. (1978) pp. 569–
587
27.7
E.B. Thornton, R.T. Guza: Transformation of wave
height distribution, J. Geophys. Res. 88, 5925–5938
(1983)
27.8
D.T. Resio: The estimation of wind-wave generation in a discrete spectral model, J. Phys. Oceanogr.
2(4), 510–525 (1981)