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. Wiegel (1962) used a theoretical 

 approach to study wave diffraction around a single breakwater. Blue and 

 Johnson (1949) dealt with the problem of the behavior of waves 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. 



2.42 DIFFRACTION CALCULATIONS 



2.421 Waves Passing a Single Breakwater . From a presentation by Wiegel 

 (1962), diffraction diagrams have been prepared which, for a uniform depth 

 adjacent to an impervious structure, show lines of equal wave height re- 

 duction. These diagrams are shown in Figures 2-28 through 2-39; the graph 

 coordinates are in units of wavelength. Wave height reduction is given in 

 terms of a diffraction coefficient K' which is defined as the ratio of a 

 wave height H, in the area affected by diffraction to the incident wave 

 height H^, in the area unaffected by diffraction. Thus, H and H^ are 

 determined by H = K'H^. 



The diffraction diagrams shown in Figures 2-28 through 2-39 are con- 

 structed in polar coordinate form with arcs and rays centered at the struc- 

 ture's tip. The arcs are spaced one radius -wavelength unit apart and rays 

 15 apart . In application, a given diagram must be scaled up or down so 

 that the particular wavelength corresponds to the scale of the hydrographic 

 chart being used. Rays and arcs on the refraction diagrams provide a 

 coordinate system that makes it relatively easy to transfer lines of 

 constant K' on the scaled diagrams. 



When applying the diffraction diagrams to actual problems, the wave- 

 length must first be determined based on the water depth at the tip of the 

 structure. The wavelength L, in water depth dg, may be found by com- 

 puting dg/L^ = dg/5.12T2 and using Appendix C, Table C-1 to find the 

 corresponding value of dg/L. Dividing dg by dg/L will give the shallow 

 water wave length L. It is then useful to construct a scaled diffraction 



2-81 



