IV. WAVE DIFFRACTION 



1 . Introduction . 



Diffraction of water waves is a phenomenon in which energy is transferred 

 laterally along a wave crest. It is most noticeable where an otherwise reg- 

 ular train of waves is interrupted by a barrier such as a breakwater or small 

 island. 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 unchanged in form 

 and height. The line separating two regions would be a discontinuity. A part 

 of the area in front of the barrier would, however, be disturbed by both the 

 incident waves and by those waves reflected by the barrier. The three regions 

 are shown in Figure 2-26(a) for the hypothetical case if diffraction did not 

 occur, and in Figure 2-26(b) for the actual phenomenon as observed. The 

 direction of the lateral energy transfer is also shown in Figure 2-26(a). 

 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 break- 

 water 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 dif- 

 fraction process is essential in planning such facilities. The 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 the shore is affected by diffraction caused by 

 naturally occurring changes in hydrography. An aerial photograph illustrating 

 the diffraction of waves by a breakwater is shown in Figure 2-27. 



Putnam and Arthur ( 1948) presented experimental data verifying a method of 

 solution proposed by Penny and Price (1944) for wave behavior after passing a 

 single breakwater. Wlegel (1962) used a theoretical approach to study wave 

 diffraction around a single breakwater. Blue and Johnson (1949) dealt with 

 the problem of wave behavior after passing through a gap, as between two 

 breakwater arms. 



The assumptions usually made in the development of diffraction theories are 



(1) Water is an ideal fluid; i.e., Inviscid and incompressible. 



(2) Waves are of small amplitude and can be described by linear 

 wave theory. 



(3) Flow is irrotational and conforms to a potential function, 

 which satisfies the Laplace equation. 



(4) Depth shoreward of the breakwater is constant. 



2-75 



