diagram shoreward to the breakwater; (b) at this point, constructing a 

 diffraction diagram carrying successive crests three or four wavelengths 

 shoreward, if possible; and (c) with the wave crest and wave direction 

 indicated by the last shoreward wave crest determined from the diffraction 

 diagram, constructing a new refraction diagram to the breaker line. The 

 work of Mobarek (1962) on the effect of bottom slope on wave diffraction 

 indicates that the method presented here is suitable for medium-period 

 waves. For long-period waves the effect of shoaling (Section 2.32) should 

 be considered. For the condition when the bottom contours are parallel to 

 the wave crests, the sloping bottom probably has little effect on diffrac- 

 tion. A typical refraction-diffraction diagram and the method for deter- 

 mining combined refraction-diffraction coefficients are shown in Figure 

 2-59. When a wave crest is not of uniform height, as when a wave is under- 

 going refraction, a lateral flow of energy - wave diffraction - will occur 

 along the wave crest. Therefore diffraction can occur without the wave 

 moving past a structure although the diffraction effects are visually more 

 dramatic at the structure. 



2.5 WAVE REFLECTION 



2.51 GENERAL 



Water waves may be either partially or totally reflected from both 

 natural and manmade barriers. (See Figure 2-60.) Wave reflection may 

 often be as important a consideration as refraction and diffraction in the 

 design of coastal structures, particularly for structures associated with 

 development of harbors. Reflection of waves implies a reflection of wave 

 energy as opposed to energy dissipation. Consequently, multiple reflections 

 and absence of sufficient energy dissipation within a harbor complex can 

 result in a buildup of energy which appears as wave agitation and surging 

 in the harbor. These surface fluctuations may cause excessive motion of 

 moored ships and other floating facilities, and result in the development 

 of great strains on mooring lines. Therefore seawalls, bulkheads and 

 revetments inside of harbors should dissipate rather than reflect incident 

 wave energy whenever possible. Natural beaches in a harbor are excellent 

 wave energy dissipaters and proposed harbor modifications which would 

 decrease beach areas should be carefully evaluated prior to construction. 

 Hydraulic model studies are often necessary to evaluate such proposed 

 changes. The importance of wave reflection and its effect on harbor 

 development are discussed by Bretschneider (1966), Lee (1964), and 

 LeMehaute (1965) ; harbor resonance is discussed by Raichlen (1965) . 



A measure of how much a barrier reflects waves is given by the ratio 

 of the reflected wave height H^, to the incident wave height H^ which 

 is termed the reflection coefficient xJ hence x = H^j/H^. The magnitude 

 of X varies from 1.0 for total reflection to for no reflection; how- 

 ever, a small value of x does not necessarily imply that wave energy is 

 dissipated by a structure since energy may be transmitted through such 

 structures as permeable, rubble-mound breakwaters. A transmission co- 

 efficient may be defined as the ratio of transmitted wave height H^, to 

 incident wave height H^. In general, both the reflection coefficient 



2-110 



