designated as H/H'o. or Tables of the Functions 

 of d/L and djLo, HE-1 16-265.) 



Table 1 

 Coefficient of shoaling, D 



d/L, 0.002 0.005 0.007 0.01 0.02 0.04 



D 2.12 1.69 1.57 1.45 1.23 1.06 



d/L„ 0.056 0.08 0.1 0.15 0.2 0.3 0.4 



D 1.0 . 94 . 92 .91 .92 .93 .96 



The graphical or analytical determination of 

 wave refraction coefficients assumes (1) that the 

 velocity of the wave crest depends only upon the 

 still water depth under the crest at each point, 

 (2) that the wave crest advances perpendicular to 

 itself, and (3) that the wave energy is confined 

 between orthogonals. 



REFRACTION AT A STRAIGHT SHORE LINE 



When the shore line and offshore contours are 

 straight and parallel, refraction may be treated 

 analytically by utilizing what is known as Snell's 

 Law, 



Sin a __C 

 Sin aa C„ 



Here, a is the angle between the wave crest and 

 the shore line in a depth such that the wave 

 velocity is C (fig. 3). The change in angle deter- 

 mines the increase in crest length, and thus the 

 value of Ka is fixed by the depth, which deter- 

 mines C for a particular Co, and a,,, the angle in 

 deep water. Referring to figure 3, the value of 

 Ki may be computed from the relationship. 



Cos tto 



= 6. 



"Cos a 



or 



where 



„ _ /6„_ /Cos ao 



^^'—\b"-^^co^ 



-(^^Sina„) 



= Sin 



For example, if ao = 45° and the depth and period 

 at the point for which Ka is to be computed, are 

 such that C/Co= 0.5, 



a=Sin-' (0.5X0.71) =20.8 deg. 



Cos a! = 0.935 and Cos a„=0.707 



no^o 



sinoC 



b. _ _ b 



COSoCo ® COSoC 



ORTHOGONALS 



V77777777777777777777777777777777 



SHORELINE 



Figure 3. — Wave refraction assuming a gradual change in wove 

 velocity. 



For convenience the relationship between a, 

 ao, depth, period, and Ka have been summarized 

 in graphical form in plate II, Breakers and Surf. 

 This graph is included herein as figure 4. 



A thorough understanding of the nature and 

 magnitude of refraction effects at straight coast 

 lines is helpful in constructing refraction diagrams 

 for complex hydrography. The beginner should 

 study figure 4 in order to develop judgment 

 regarding the hydrographic conditions necessitat- 

 ing graphical analysis and as a basis for checking 

 approximately the numerical values of K^ result- 

 ing from a graphical determination. 



It is noteworthy that, on a straight shore line, 

 the reduction in wave height by refraction is less 

 than 10 percent when the initial angle in deep 

 water is less than 36 degrees. 



CONSTRUCTION OF REFRACTION DIAGRAMS 



Ideal waves in deep water move forward with 

 their crests parallel, but over a shoaling bottom 

 the reduction in wave velocity causes the crest 

 to swing around in the direction which will 

 decrease the angle between the crest and the bot- 

 tom contour. The preceding statement obvi- 

 ously requires a quantitative definition of what is 

 meant by "deep water" and by "shallow water." 

 The usual definition is that in 



deep water, d^-^ 



shallow water, d<^-^ 





