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WAVES AT PORTS AND HARBORS*
C. L. Vincent
Introduction
Estimation of shortperiod (1 to 30 second) waves in the vicinity
of ports and harbors can be made difficult by the same features of the
physical environment that make the site desirable for port development.
Ports are often located in areas with shallow and highly irregular
bathymetry. Additionally, the shoreline or harbor configuration may be
geometrically complex, and there may be strong tidal or riverine
currents. As a result, practically all the simplifying assumptions
used to make wave calculations tractable do not hold.
In thin presentation, I wish to discuss the state of the art in
estimating wave conditions in port areas, and direct your attention to
areas where work is needed. I wish to emphasize two areas: developing
a wave climate and modeling waves. I will cite a few papers, but this
presentation is not intended to be a review of the subject. Further,
it must be clear that the solution of the wave problem depends heavily
on knowledge of the water level, currents, and bathymetry.
Developing a Wave Climate
For the purpose of port design, it is necessary to know the general
wave climate of the area. For the purposes of modeling, it ~s
desirable to have information not only on wave heights and periods but
wave directions as well. The data should be climatological and they
should contain information on extremes and information on the
daytoday wave climate. Information on longterm climate variations
may be helpful if sediment transport problems are to be addressed.
Information on wave grouping is desirable as well. Two questions
require attention. First, how does one obtain the basic data, and
second, how does one statistically treat quantities such as directional
spectral characteristics?
*This summary i" based on re~earob performed under the coastal
engineering program of the U.S. Army Corps of Engineers. Permission to
publish this information i" appreciated.
133
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134
It is helpful to start the discusaion by looking at how wave data
can be obtained in tbe region of the harbor. In general, there is very
little onedimensional wave data available on which to base a wave
climate, and almost no directional data. Either an extensive gaging
program extending ten to twenty years must be establiabed, or the
designer must go to a synthetic climate obtained through hindcast
techniques. In the deep water case, significant progress ha" been made
in the development of bindca~t models, especially in predicting
spectral characteristics. Several models are listed in Table I. In
applications involving large storms, the root mean square (RMS) error
in prediction is of the order of 1 meter, which is generally
satisfactory for climate estimates of extremes. These models require
very large computers. A major limitation in the application of the
models is lack of knowledge of the meteorology, particularly on the
oceanic scale.
The next stage, if simulations must be used, is to begin modeling
wave growth, transformation, and decay in shallow water. Modeling may
be needed even if some gage data are available. If the bathymetry is
complex, or if strong currents are present, gage data tends to be
sitespecific and not readily extrapolated or interpolated. These
modeling problems will be discussed in the next section.
Although the limitations of gaging need to be recognized,
significant advances have been made in instrumentation to make it
reliable and reasonable in cost. Remote sensing techniques can also be
very useful. The example of sidelooking imaging radar given in Figure
1 shows in great detail patterns of refraction, diffraction, and
breaking. Many of these instruments can operate in poor weather
conditions, and can give a designer an improved picture of wave
activity in the port area. Because the bathymetry may be complex and
the wave field irregular, data from remote sensing systems may be
useful in deciding where to place gages and in interpreting gage
results.
The data synthetically produced by bindcast models or measured
directly by gaging programs can provide the wealth of data required to
understand waves at ports and harbor entrances. The data extend beyond
providing just significant wave heights and periods to aspects of
directionality and grouping. It is not yet clear what methods are best
for statistically analyzing and displaying these data. Indeed, such
questions as definition of ~ design spectrum are not uniformly answered.
Modeling Teabnigues
Two classes of methods for modeling wave problems will be
discuseeds numerical and physical modeling. The advantages and
disadvantages are presented. It is essential to remember that both
methods entail simulations in which a large number of simplifications
are made.
The primary causes of the difficulties in numerical modeling of
waves lie in the irregularity of the bathy~etry, the presence of
current, and nonlinearities of the waves. One problem is the
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Figure 1. Waves on Ebb Jet, at the mouth of the Columbia River. SLAR
(sidelooking airborne radar) image provided by Dr. C. Rosenfeld, Oregon
State National Guard Remote Sensing Group.
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136
TABLE 1 SOME DEEP WATER SPECTRAL PREDICTION MODELS
PUBLISHED
DEVELOPER/REFERENCE PRIMARY USE ERROR CHARACTERISTICS
.
(in hindcast mode)
Fleet Numerical Oceanographic
Center Ocean up to 3 m
Salfi (1974)
Waterway" Experiment Station
Resio and Vincent (1977) Lakes 0.5 m
Resio and Vincent (1979) Ocean 1.5 m
Cardone et al (1975) Hurricane 1.5 m
Hybrid parametric North Sea 0.9 m
Gunther et al (1979)
refractiondiffraction of waves. Almost all practical numerical models
of waves require that the rate of change of bottom slope be small with
respect to the wave length. Even if thin constraint is only mildy
violated, the modeling of the bathymetry requires a dense grid mesh,
thereby creating a large computation problem. In deep water, the
effects of nonlinearities appear significant in determining wave
growth. Research underway by Heterich and Hasselmann suggests that
these nonlinearities are also important in shallow water, which if
correct, complicates spectral modeling, requiring crossspectral
transfers. One final, and so far intractable, problem in improved
treatment of wave breaking.
Two approaches to the numerical modeling of waves in shallow water
are now used. The first is the spectral approach. There are several
models available that treat this problem {Table 2~. The Hsaio model
allows intraspectral energy transfers; Wang and Yang allows currents ;
none treats diffraction. The advantage of the spectral techniques is
that they consider the entire wave spectrum, and can treat the effects
of refraction of each wave component. One disadvantage occurs largely
because this type of modeling is "till under development and the
refraction part of the algorithm is normally primitive. A second
disadvantage in that the algorithm is complicated, and can require
large amounts of computer storage and run time.
The second type of numerical model normally is used to treat only
one wave component. In this class, four types are available: ray,
finite differences, finite element, and Boussinesq finite difference
models. Examples are provided in Table 3. Both ray and finite
differences models based on linear refraction theory are reasonably
well known and are used in standard engineering design worldwide. The
most significant problem with these models is that they do not treat
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137
TABLE 2 SOME SHALLOWWATER SPECTRAL MODELS
DEVELOPER/REFERENCE
Collins and Weir (1972)
Hsaio (1978)
Wang and Yang (1977)
MECHANISMS INCLUDED
Wave growth' refraction
shoaling, bottom friction
Wave growth, refraction,
shoaling, various bottom
interaction terms
Refraction, shoaling
TABLE 3 SOME REGULAR WAVE PREDICTION MODELS
DEVELOPER/REFERENCE
Birkemeier and Dalrymple {1975)
Poole et al (1977)
Berkhoff (1972)
Houston {1980)
Abbott et al (1978)
TYPE
Finite difference linear refraction'
currents
Linear refraction, rays
Finite element refraction 
diffraction
Finite element refraction
diffraction

Finite difference r refraction
diffraction and amplitude
effects (Boussinesq terms)

diffraction, and in areas of irregular bathymetry can give misleading
answers. Breaking is normally treated with a deptblimiting criterion
The other two types of models do handle aspects of the refraction
diffraction problem. In the Bous~inesq approach of Abbott, the
.
equations treat effect" of amplitude on dispersion as well as refraction
and diffraction. The finite element models are based on linear theory,
but more effectively handle irregular geometries and reflected waves
than the Boussinesq model. The finite element model" are steadystate
models, while the Boussinesqtype model is a timemarching scheme. The
advantage of both techniques is that they provide a more accurate model
of the waves. The disadvantage is cost. These models require grid
mesh or element sizes of the order of onetenth the wave length. At
this time, their use appears justified for small areas or for large
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areas when just a few cases are run. The incorporation of current
ef feats has not been widely explored. An ideal numerical model would
provide the effects of amplitude, as in the Boussinesq model, handle
boundaries and reflected waves with the ease of the finite element
models, but use a telescoped grid mesh that would allow large gridmesh
values in areas of least interest. Unfortunately, such a model does
not yet exist.
The other major approach to investigating waves at port entrances
is the use of an undistorted physical model based on a Froude scaling
law. These models by their nature handle the refractiondiffraction
and nonlinear problems through scale modeling. Currents may also be
included. Breaking occurs naturally as well, although it is not clear
that wave reformation and waveenergy dissipation are correctly modeled.
In any case, this model's estimates are probably closer than those of
any numerical model.
Areas in which physical modeling could be improved are through the
use of irregular waves with a directional spread, and simulation of
wave grouping. If conditions that include significant breaking are
modeled, model verification studies should possibly be encouraged. The
major disadvantages of the physical model are its cost and the time
required for construction and testing. In the case of large harbors,
however, there is little other choice.
Summary
The advent of numercial models and improved instrumentation should
lead to an improvement in our ability to estimate wave conditions in
port and harbor entrances; however, for many problems, a physical model
appears the most effective solution. Researab is required to extend
the applicability of numerical models and to develop more economical
solution techniques. Research is also required to improve simulation
of irregular waves in physical models.
REFERENCES
Abbott, M. B., H. M. Petersen, and O. Sko~gaard, non the Numerical
Modeling of Short Waves in Shallow Water, n Journal of Hydraulic
Researab, 16 (19781: 173204.
Birkemeier, W. A. and R. A. Dalrymple, "Nearsbore Water Circulation
Induced by Wind and Waves," ASCE Symposium on Modeling Techniques,
San Francisco, pp. 10621081.
Berkhoff, C. W., Computation of Combined RefractionDiffraction,.
Proceedings of 13th International Conference on Coastal
Engineering, Vancouver, Canada, 1972.
Cardone, V. J., W. J. Pierson, and E. G. Ward, "Hindcasting the
Directional Spectra of Hurricane Generated Waved (OTC 2332)
Offshore Teabnology Conference, 1975.
Collins, J. I. and W. Weir, "Prediction of ShallowWater Spectra,
Journal of Geophysical Research, 77 (1972~: 26942706.
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139
Gunther, H., W. Rosenthal, T. J. Weare, B. A. Worthington, K. Hasselmann
and J. A. Ewing, "A Hybrid Parameterized Wave Prediction Model,"
Journal of Geophysical Research, 84 {1979~: 57275738.
Houston, J. R., "Modeling of Short Waves Using the Finite Element
Methods Proceedings, Third International Conference on Finite
Elements in Water Resources, 1980, pp. 5.1815.195.
Hsaio, S. V., On the Transformation Mechanisms and the Prediction of
FiniteDepth Water Waves, University of Florida Doctoral
Dissertation, 1978.
Poole, L. R. et al., ~MinimalResource Computer Program for Automatic
Generation of Ocean Wave Ray at Crest Diagrams in Shoaling Waters"
(NASA Technical Memorandum 74076), Washington, D.C., National
Aeronautics and Space Administration, 1977.
Resio, D. T. and C. L. Vincent, HA Numerical Hindcast Model for Wave
Spectra on Water Bodies with Irregular Shoreline Geometry, Report
1: Test of NonDimensional Growth Rates, n Miscellaneous Papers
H779, Hydraulics Laboratory, U.S. Army Corps of Engineers
Waterways Experiment Station, Vicksburg, Mississippi, 1977.
Resio, D. T. and C. L. Vincent, "A Comparison of Various Numerical Wave
Prediction Techniques" (OTC 3642), Offshore Technology Conference,
1979, pp. 24712481.
Salfi, R. E., Operational Computer Based Spectral Wave Specification
and Forecasting Models, n The University Institute of Oceanography
of the City University of New York, Report prepared for the SPOC
Group of the National Environmental Satellite Service, National
Oceanic and Atmospheric Administration, 1974.
Wang, H. and W. C. Yang, Measurements and Computations of Wave Spectral
Transformation at Island of Sylt, North Sea, n LeichtweirsInstitute
Fur Warserbau der Technischen Universitat Braunschineig,
Mitteilungen Heft 52, 1977.
DISCUSSION
WEBSTER: Do you have instrumentation to measure directional
spectra? How do you do that?
VINCENT: There are instruments that give measures of the
directional spectrum. We have current meters, horizontal current
meters, and pressure transducers. There are any number of arrays that
will give you some measure of the directionality of the sea. There are
pitchroll buoys, and radar techniques. The major difficulty with
these techniques seems to be that they reallyfrom the input we get
backdon't give, in many instances, a narrow enough idea of what the
wave direction is. Most of these techniques tend to spread out the
directionality. There is some debate about whether the spread is real
or an artifact of the algorithm used to generate the spectrum.
The remote sensing data tend to show much narrower spread.
So, we can get ideas of mean direction" in part of the spectrum
reasonably well, but if you need to know the very narrowness of the
spread) and perhaps even the wave direction to just a few degrees, it
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may not be possible at this time. We can certainly give you a general
idea of the direction from which the waves are coming.
WEBSTER: Can I follow that up? Does your bindcasting model
give directional information? Other than the direction of the
principal waves, will it give an idea of the spread?
VINCENT: The models I discussedal] but onecalculate for
each frequency how much energy is going in as many as 16 or 24
different directions. The problem is that normally the wind
information may not be good enough to justify finer directionality,
although the models would allow it. So, with any one frequency
component you can go to 16 or 24 points of the compass and have an
estimate of how much energy is going in each of those directions and
get a truly directional spectrum.
DEAN: One of the types of waves you didn't mention that can
be of interest to the port designer is the secondorderofforce waves
driven by groups of waves. Would any of the methods you mentioned,
say, Abbott's model, if given a group of waves to deep water, also
represent these?
VINCENT: Abbott's model is really the only one, I think, that
has the potential to do that. Again, it is limited by an Ursell
parameter. You can put an irregular wave train in Abbott's model. The
only difficulty that you have is that of specifying the boundary
conditions. Abbott claims that you should be able to derive that from
his results. As far as I know, no one has checked this.