2.422 Waves Passing a Gap of Width Less than Five Wavelengths at Normal 

 Incidence . The solution of this problem is more complex than that for a 

 single breakwater, and it is not possible to construct a single diagram 

 for all conditions. A separate diagram must be drawn for each ratio of 

 gap width to wavelength B/L. The diagram for a B/L-ratio of 2 is shown 

 in Figure 2-42 which also illustrates its use. Figures 2-43 through 2-52 

 (Johnson, 1953) show lines of equal diffraction coefficient for B/L-ratios 

 of 0.50, 1.00, 1.41, 1.64, 1.78, 2.00, 2.50, 2.95, 3.82 and 5.00. A 

 sufficient number of diagrams have been included to represent most gap 

 widths encountered in practice. In all but Figure 2-48 (B/L = 2.00), the 

 wave icrest lines have been omitted. Wave crest lines are usually of use 

 only for illustrative purposes. They are, however, required for an 

 accurate estimate of the combined effects of refraction and diffraction. 

 In such cases, wave crests may be approximated with sufficient accuracy 

 by circular arcs. For a single breakwater, the arcs will be centered on 

 the breakwater tip. That part of the wave crest extending into unprotected 

 water beyond the K' =0.5 line may be approximated by a straight line. 



For a breakwater gap, crests that are more than eight wavelengths behind 

 the breakwater may be approximated by an arc centered at the middle of 

 the gap; crests to about six wavelengths may be approximated by two arcs, 

 centered on the two ends of the breakwater and may be connected by a 

 smooth curve (approximated by a circular arc centered at the middle of 

 the gap) . Only one-half of the diffraction diagram is presented on the 

 figures since the diagrams are symmetrical about the line x/L = 0. 



2.423 Waves Passing a Gap of Width Greater Than Five Wavelengths at 

 Normal Incidence . Where the breakwater gap width is greater than five 

 wavelengths, the diffraction effects of each wing are nearly independent, 

 and the diagram (Figure 2-33) for a single breakwater with a 90° wave 

 approach angle may be used to define the diffraction characteristic in 

 the lee of both wings (See Figure 2-53.) 



2.424 Diffraction at a Gap-Oblique Incidence . When waves approach at an 

 angle to the axis of a breakwater, the diffracted wave characteristics 

 differ from those resulting when waves approach normal to the axis. An 

 approximate determination of diffracted wave characteristics may be 

 obtained by considering the gap to be as wide as its projection in the 

 direction of incident wave travel as shown in Figure 2-54. Calculated 

 diffraction diagrams for wave approach angles of 0°, 15°, 30°, 45°, 60° 

 and 75° are shown in Figures 2-55, 56 and 57. Use of these diagrams will 

 give more accurate results than the approximate method. A comparison of 



a 45° incident wave using the approximate method and the more exact diagram 

 method is shown in Figure 2-58. 



2.43 REFRACTION AND DIFFRACTION COMBINED 



Usually the bottom seaward and shoreward of a breakwater is not 

 flat; therefore, refraction occurs in addition to diffraction. Although 

 a general unified theory of the two has not yet been developed, some in- 

 sight into the problem is presented by Battjes (1968) . An approximate 

 picture of wave changes may be obtained by: (a) constructing a refraction 



2-98 



