The tennV(l/2) (1/n) (Cq/C) is known as the shoaling coefficient Kg or 

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

 depth. K_ and various other functions of d/L, such as Zird/L, Aird/L, 

 tanh(2Trd/L) , and sinh(4Trd/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, Vb^Tb, 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 per- 

 mitted moving from the shore to deep water (Johnson, O'Brien, and Isaacs, 

 1948; Arthur, Munk, and Isaacs, 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 



sin a = — sin a (Snell's law) (2-78a) 



1 



where 



°1 



= the angle a wave crest (perpendicular to an orthogonal) makes 

 with the bottom contour over which the wave is passing 



a_ = a similar angle measured as the wave crest (or orthogonal) 

 passes over the next bottom contour 



C = the wave velocity (eq. 2-2) at the depth of the first contour 



C = 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 to construct the changed-direction orthogonal. Such a template is 

 shown in Figure 2-18. In application to wave refraction problems, it is sim- 

 plest to construct this template on a transparent material. 



Refraction may be treated analytically at a straight shoreline with 

 parallel offshore contours, by using Snell's law directly: 



(2-78b) 



where a is the angle between the wave crest and the shoreline, and a^ is 

 the angle between the deepwater wave crest and the shoreline. 



For example, if a^ = 30° and the period and depth of the wave are such 

 that C/Cq = 0.5, then 



2-64 



