but, from the basic wave equation for all waves, 



L 

 T 



C = i (41) 



so that 



u = H /id = HJ^l (42) 



d * d 1/2 



The water surface elevation can also be defined as 



n = a sin T2tt (- - -Y| (43) 



so that by substituting equations (33) , (37) , and (43) into equation 

 (28), 



1 , (¥) ^ 



s = -n — ; ; (44) 



and noting again that z/L ■* 0, 



^ = - Sd C45) 



The wave energy, E, for a small -amplitude wave is given by 



E = £iJlik (46 ) 



where p is the density of the seawater. If energy is conserved between 

 two points for an unrefracted wave, 



H /L 



1/2 



i = %) t48j 



but as L = CT, and T is assumed to be constant, and as C = v/gd" for a 

 shallow-water wave, then 



h 2 /v ; 



(49) 

 H, VcL 



41 



