Refraction may be treated analytically at a straight shoreline with 

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



... -ig ... 



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

 is the angle between the deepwater wave crest and the shoreline. 



For example, if cxq = 30° and the period and depth of the wave 

 are such that C/C^ = 0.5, then 



a = sin-' [0.5 (0.5)] = 14.5 degrees 

 cos a = 0.968 



and 



cosa^ = 0.866 



cosaA'^ / 0.866 \^ 



cos a / \ 0.968 



= 0.945 



Figure 2-19 shows the relationships between a, a^, period, depth, and 

 K^ in graphical form. 



2.321 Procedures in Refraction Diagram Construction - Orthogonal Method . 

 Charts showing the bottom topography of the study area are obtained. Two 

 or more charts of differing scale may be required, but the procedures are 

 identical for charts of any scale. Underwater contours are drawn on the 

 chart, or on a tracing paper overlay, for various depth intervals. The 

 depth intervals chosen depend on the degree of accuracy desired. If 

 overlays are used, the shoreline should be traced for reference. In 

 tracing contours, small irregularities must be smoothed out, since bottom 

 features that are comparatively small in respect to the wavelength do not 

 affect the wave appreciably. 



The range of wave periods and wave directions to be investigated is 

 determined by a hindcasting study of historical weather charts or from 

 other historical records relating to wave period and direction. For each 

 wave period and direction selected, a separate diagram must be prepared. 

 C1/C2 values for each contour interval may then be marked between contours, 

 The method of computing C1/C2 is illustrated by Table 2-2; a tabulation 

 of C1/C2 for various contour intervals and wave periods is given in 

 Table C-4 of Appendix C. 



To construct orthogonals from deep to shallow water, the deepwater 

 direction of wave approach is first determined. A deepwater wave front 

 (crest) is drawn as a straight line perpendicular to this wave direction. 



2-69 



