much larger than water depths in the region treated, and the numerical value 

 in metric units of (HjT^) = 32.6, nearly twice the maximum water depth con- 

 sidered in meters, so that equation (12) indicates rough turbulent flow 

 throughout the region. The calculation procedure is suitable for these con- 

 ditions, and the effect of bottom friction on wave shoaling is appreciable, 

 in that linear wave theory without dissipation would predict a nearshore wave 

 height of (Hi Kg^/K ,) = [ (3.5) (0.9779) /O. 9160] =3.74 meters, using equation 

 (5). -* 



(b) For Ti =14.0 seconds and d^ = 18 meters, (d^/L^) = 0.05882 so that 

 ni = 0.8833, (Hi/H^) = 0.9963 = Kg^, (d^/L^) = 0.1031 and L^ = 174.6 meters 

 from Table C-1. Equation (2) with Hj = 3.5 meters gives 



P J = ^ (1026) (9.81) (3.5) 2 ^^^ (0.8833) 



= 1.70 • 10^ kilogram-meter per second cubed 



At d^, (d^j/Lg) = 0.04160 so that (d^/L^) = 0.08509, sinh (2vdj^fLj = 0.5605, 

 (Hjj/H^) = 1.057 = Kgjn, and n = 0.9161. Thus, H^ = (H^ Ksm/Ksi) = 3.71 meters, 

 equation (9) is 



3.71 



Ln - = 3.31 meters 



2(0.5605) 



equation (8) is 



fgnj = exp {-5.882 + 14.57 (1.2 • 10-'+/3.31) « • ^5'+} = 0.0207 

 and equation (7) is 



E^ = (0.235) (1026) (0.0207) ^^f^l^ I 



= 16.36 kilograms per second cubed 



At dj, (dj/Lo) = 0.02941 so that (Hj/H^) = 1.130 = Kg j , nj = 0.9400, 

 (dj/Lj) = 0.0706 and Lj = 127.5 meters. Again, the lower sign in equation 

 (10) is used to give 



2 _ 8[1.70 ' 105 - (16.36) (1800)] ...^ 

 H. - — = 13.05 square meters 



(1026) (9.81) [ll^Q^ (0.9400) 

 H. = 3.61 meters 



Because T is greater here than in part (a) , the requirements for rough 

 turbulent flow at a strongly agitated sand bed are clearly satisfied. Although 

 the computation including friction results in H-! slightly larger than H^ 

 in this case, energy dissipation again has an appreciable effect since linear 

 wave theory would predict a nearshore wave height of (H-^ Kgj/Kg^j) = 3.97 meters, 

 from equation (5) . 



12 



