Pierson (1951), Longuet-Higgins (1957), and Kinsman (1965), have sug- 

 gested a solution to the ocean-wave refraction problem. The sea surface 

 waves in deep water become a number of component monochromatic waves, each 

 with a distinct frequency and direction of propagation. The energy spec- 

 trum for each component may then be found and the conventional refraction 

 analysis techniques applied. Near the shore, the wave energy propagated 

 in a particular direction is approximated as the linear sum of the spectra 

 of wave components of all frequencies refracted in the given direction from 

 all of the deepwater directional components. 



The work required for this analysis, even for a small number of indi- 

 vidual components, is laborious and time consuming. More recent research 

 by Borgman (1969) and Fan and Borgman (1970), has used the idea of direc- 

 tional spectra which may provide a technique for solving complex refraction 

 problems more rapidly. 



2.4 WAVE DIFFRACTION 



2.41 INTRODUCTION 



Diffraction of water waves is a phenomenon in which energy is trans- 

 ferred laterally along a wave crest. It is most noticeable where an other- 

 wise regular train of waves is interrupted by a barrier such as a breakwater 

 or an islet. If the lateral transfer of wave energy along a wave crest and 

 across orthogonals did not occur, straight, long-crested waves passing the 

 tip of a structure would leave a region of perfect calm in the lee of the 

 barrier, while beyond the edge of the structure the waves would pass un- 

 changed in form and height. The line separating two regions would be a 

 discontinuity. A portion of the area in front of the barrier would, how- 

 ever, be disturbed by both the incident waves and by those waves reflected 

 by the barrier. The three regions are shown in Figure 2-26a for the hypo- 

 thetical case if diffraction did not occur, and in Figure 2-26b for the 

 actual phenomenon as observed. The direction of the lateral energy trans- 

 fer is also shown in Figure 2-26a. Energy flow across the discontinuity 

 is from Region II into Region I. In Region III, the superposition of 

 incident and reflected waves results in the appearance- of short-crested 

 waves if the incident waves approach the breakwater obliquely. A partial 

 standing wave will occur in Region III if the waves approach perpendicular 

 to the breakwater. 



This process is also similar to that for other types of waves, such 

 as light or sound waves. 



Calculation of diffraction effects is important for several reasons. 

 Wave height distribution in a harbor or sheltered bay is determined to 

 some degree by the diffraction characteristics of both the natural and 

 manmade structures affording protection from incident waves. Therefore, 

 a knowledge of the diffraction process is essential in planning such 

 facilities. Proper design and location of harbor entrances to reduce 

 such problems as silting and harbor resonance also require a knowledge 

 of the effects of wave diffraction. The prediction of wave heights near 



2-79 



