THE ELEVATION AND DURATION OF WAVE CRESTS 



by 

 William N. Seelig, John P. AhrenSj and William G. Grosskopf 



I . INTRODUCTION 



Coastal structures are generally built to withstand extreme waves that 

 occur infrequently. One of the important aspects of these waves is that they 

 may be highly nonlinear if the wave steepness is large or the relative water 

 depth is small. Two of the important engineering characteristics of nonlinear 

 waves are that the crest elevations are more than half of the wave height and 

 the duration of the crests are less than half of the wave period. 



Crest elevation is important because the forces on a structure may be more 

 strongly related to crest elevation above the water level than the trough dis- 

 tance below the water level. Uplift forces on piers and fixed structures 

 are particularly sensitive to wave crest elevation, which is one of the reasons 

 why most offshore platforms and piers are built well above the water level. 

 Crest elevation also influences wave runup and overtopping (Weggel, 1976a). 



The relatively short duration of nonlinear wave crests is important, 

 because the combination of high elevation and short duration produces large 

 water particle motions and accelerations. These hydraulic characteristics have 

 the potential for suspending sediment, lifting armor units, and causing surpris- 

 ingly high drag forces on coastal structures. 



Figure 1 is a sample wave record made as part of the Coastal Engineering 

 Research Center's (CERC) coastal wave collection program (Thompson, 1977). 

 This example clearly shows the high crest elevations and short crest durations 

 that may occur in coastal waters. 



This study develops methods of predicting crest elevations and duration for 

 monochromatic and irregular waves. Laboratory waves are used to minimize the 

 influence of refraction, diffraction, irregular topography, directional spread 

 of wave energy, and multiple wave trains on the characteristics of wave crests. 

 Assumed independent variables used in the prediction methods are water depth, 

 wave period or period of peak energy density for irregular waves, wave height 

 (significant wave height for irregular waves), and beach slope. Predictions 

 are compared to selected prototype wave measurements taken at the CERC Field 

 Research Facility (FRF) at Duck, North Carolina. 



II. LITERATURE REVIEW 



Goda (1964) performed some basic research on the elevation of monochromatic 

 laboratory wave crests. Using his own data and the data of Bretschneider (1958). 

 Goda found that the ratio of wave height to water depth played a dominant role 

 in determining the relative crest elevation. However, there are considerable 

 scatter in the results. 



Jahns and ITheeler (1973) and others have performed theoretical derivations 

 of expected crest heights for irregular wave conditions. Without including 

 nonlinear effects they conclude that a Rayleigh-type distribution should 



