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WAVES AT PORTS AND HARBORS* C. L. Vincent Introduction Estimation of short-period (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 day-to-day wave climate. Information on long-term 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

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 one-dimensional 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 site-specific 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 side-looking 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

~ - i `~ - - ;~ At ~- ~ ~ . ~ ~ Jo 135 - -_~ red F .~ ~ a! _ ~ ' Figure 1. Waves on Ebb Jet, at the mouth of the Columbia River. SLAR (side-looking airborne radar) image provided by Dr. C. Rosenfeld, Oregon State National Guard Remote Sensing Group.

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) refraction-diffraction 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 cross-spectral 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

137 TABLE 2 SOME SHALLOW-WATER 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 deptb-limiting 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 steady-state models, while the Boussinesq-type model is a time-marching 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 one-tenth the wave length. At this time, their use appears justified for small areas or for large

138 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 grid-mesh 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 refraction-diffraction 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 wave-energy 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: 173-204. Birkemeier, W. A. and R. A. Dalrymple, "Nearsbore Water Circulation Induced by Wind and Waves," ASCE Symposium on Modeling Techniques, San Francisco, pp. 1062-1081. Berkhoff, C. W., Computation of Combined Refraction-Diffraction,. 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 Shallow-Water Spectra, Journal of Geophysical Research, 77 (1972~: 2694-2706.

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~: 5727-5738. Houston, J. R., "Modeling of Short Waves Using the Finite Element Methods Proceedings, Third International Conference on Finite Elements in Water Resources, 1980, pp. 5.181-5.195. Hsaio, S. V., On the Transformation Mechanisms and the Prediction of Finite-Depth Water Waves, University of Florida Doctoral Dissertation, 1978. Poole, L. R. et al., ~Minimal-Resource 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 Non-Dimensional Growth Rates, n Miscellaneous Papers H-77-9, 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. 2471-2481. 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 Leichtweirs-Institute 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 pitch-roll buoys, and radar techniques. The major difficulty with these techniques seems to be that they really--from the input we get back--don'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

140 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 discussed--al] but one--calculate 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 second-order-of-force 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.