spacinp- bett'TSsn the two lines in shallow i-fater. Therefore 1/2 b 



n b E or 



"! 

 X -~ 







E., 2 n b (7) 



■To 



(a) PI/II = / '■^T Y o , tharef'ore equation (7) rany be 



rom eauataon , 



"" I E„ - L 

 V To 



written 



H/K = y J:.,. X i_ X ^ (V b A ) 



'0 2nL ^o' ' 



The tern v'' 1/2 x l/n"L 7L ' is loiown as the shoal3.nK coefficient (H/lI ')» 

 It is a function of d./L and may te found in Table 1 of A-ooendis D .- 



26.S Equation (8) shot.>rs that wave heights in transitional or shallow 

 water raaj be foimd, Icnowing deep water wave heightSj if the relative spac- 

 ing between lines drawn perpendicular to x^ave crests can be determined. - 

 The square root of this relative spacing (b /b) is known as the refraction 

 coefficient. It shortld also be noted that "ohese perpendicular lines, when 

 constructed, T-jill show the direction of itiover,Bnt of the waves to whj.ch 

 they are drawn perpendicular*. 



27.- The lines dra>m perpendicular to the wave crests are known as 

 orthogonals . Ynrious iisethods have been proposed for constructing these 

 lines. The earlier approaches required dramng positions of wave cresi.Sj 

 then erecting perpendiculars to them: later approaches eli.ird.nate the 

 intermediate wave crest step, permitting the im-ediate construction of 

 orthogonals thenselveSi 



28s It can 'be sliOT-m (Appendix E) that the change of direction of an 

 orthogonal as it passes over relatively simple -andenTater topography is 



sina^ = G^/G^ sina^ ^^^^ 



where a is the angle a normal to an orthogonal mal<:es "jith a contour the 

 ~ orthogonal is passing over, 

 a^ is a siEiilar angle measured as tlie orthogonal passes over the nex-b 



contour 

 C, is the wave velocity (equation 1) at the depth of the first 



contour, ard 

 C^ is the i'J9Ye velocity at the depth of the second contoij.r. 



From tba.s equation, a template may be constructed i-fith v^Mch the angxiLar 

 change in o- as an orthogonal passes over a defirrlte contour interval may 

 be found, and the changed-direction-orthogonal rtiay be constructed, (see 

 Appendix S), Such a template is shown on Figure 12, 



19 



