and combining Equations 2-75 and 2-76, 



H_ 

 Ho 



(2-77) 



The term /(1/2) (1/n) (C^/C)' is known as the shoaling coefficient Kg 

 or H/H^. This shoaling coefficient is a function of wavelength and water 

 depth. Kg and various other functions of d/L, such as 2T7d/L, 47rd/L, 

 tanh(27rd/L) , and sinh(4TTd/L) are tabulated in Appendix C, (Table C-1 for 

 even increments of d/L^, and Table C-2 for even increments of d/L). 



Equation 2-77 enables determination of wave heights in transitional 

 or shallow water, knowing the deepwater wave height when the relative 

 spacing between orthogonals can be determined. The square root of this 

 relative spacing, /b^/b', is the refraction coefficient K^. 



Various methods may be used for constructing refraction diagrams. 

 The earliest approaches required the drawing of successive wave crests. 

 Later approaches permitted the immediate construction of orthogonals, 

 and also permitted moving from the shore to deep water (Johnson, O'Brien 

 and Isaacs, 1948), (Arthur, et al . , 1952), (Kaplan, 1952) and (Saville 

 and Kaplan, 1952) . 



The change of direction of an orthogonal as it passes over relatively 

 simple hydrography may be approximated by 



sina, = M- 



sin a (Snell'slaw) (2-78) 



where ; 



a^ is the angle a wave crest (the perpendicular to an orthogonal) 

 makes with the bottom contour over which the wave is passing, 



a^ is a similar angle measured as the wave crest (or orthogonal) 

 passes over the next bottom contour, 



C, is the wave velocity (Equation 2-2) at the depth of the first 

 contour, and 



C2 is the wave velocity at the depth of the second contour. 



From this equation, a template may be constructed which will show the 

 angular change in a that occurs as an orthogonal passes over a 

 particular contour interval, and construct changed-direction orthogonal. 

 Such a template is shown in Figure 2-18. In application to wave refrac- 

 tion problems, it is simplest to construct this template on a transparent 

 material. 



2-67 



