the incident wave direction and presents diffraction diagrams for various gap 

 widths. This work and the resulting diffraction diagrams are presented in 

 Chapter 7. 



3. 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 only been developed for a few special cases, 

 some insight into the problem is presented by Battjes (1968), and Berkoff 

 (1972). Battjes (1968) shows that contrary to what numerous investigators 

 have stated, there is no lateral transfer of energy along a wave crest but 

 that all energy flux is along an orthogonal. Berkoff (1972) develops the 

 equations that govern the combined refraction-diffraction phenomenon and uses 

 finite-element models to numerically calculate the propagation of long waves 

 around an Island and over a parabolic shoal. He also investigated the 

 response of a rectangular harbor with constant bottom slope to incident shore 

 waves . 



More recently, Ilu and Lozano (1979), Lozano (1980), and Liu (1982) studied 

 analytically the behavior of waves in the vicinity of a thin groin extending 

 seaward from a sloping beach. Liu (1982) compared their analytical results 

 with the experimental data obtained by Hales ( 1980) of combined refraction- 

 diffraction around a jetty on a sloping beach with good agreement. Lozano and 

 Liu ( 1980) compared the analytical solution with experimental data obtained by 

 Whalin (1972) for wave propagation over a semicircular shoal, again with good 

 agreement in the shadow region of the structure. An approximate picture of 

 wave changes may be obtained by (a) constructing a refraction diagram shore- 

 ward 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 refrac- 

 tion 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 shoal- 

 ing (Sec. 111,2) should be considered. For the condition when the bottom con- 

 tours are parallel to the wave crests, the sloping bottom probably has little 

 effect on diffraction. A typical refraction-diffraction diagram and the 

 method for determining combined refraction-diffraction coefficients are shown 

 in Figure 2-61. 



V. WAVE REFLECTION 



1. General. 



Water waves may be either partially or totally reflected from both natural 

 and manmade barriers (see Fig. 2-62). Wave reflection may often be as impor- 

 tant a consideration as refraction and diffraction in the design of coastal 

 structures, particularly for structures associated with harbor development. 

 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 



2-109 



