changes in wave height depend uDon changes in the rate at vhich 



energy advances. In deep water the amount of energy which 



advances through a cross section of the wave is 1/2 C E , where 

 ' o o ' 



C = /tt^ L„ and E is the luean energy of the wave Der unit 



surface area. In shallow water the corresoonding amount is C E 



s s 



where C \S'^' If" ^o energy is lost by bottom fraction as the 



wave advances toward shore, 1/2 C E = C E . Where E = E , one 



' o o s s o s ' 



has 1/2 C = C or 1/2 L = L . The corresnonding deoth is 



O S ' O S - to . 



d = 



= Lo . — ^^ /~^, ^s . 

 "g7r"^25 12.5 

 Therefore, the wave height, which is pronortional to the 



square root of the wave energy, is the same in deep water and in 



shallow water where the denth is aoDroximately L /2 5. The wave 



height however does appear higher. The steeoness of the wave has 



been doubled because the wave length has decreased one half. 



As the depth becomes less than L /25 the wave height increases 



o ^ 



raoidly and the wave length continues to decrease. When long and 

 lov; sv;ell approaches a gently sloping beach, narrow, steep crests, 

 separated by long, flat troughs, appear to rise a short distance 

 from the beach, and these crests soon become so steep that they 

 break. It is the narrowness, however, and not the height of the 

 crests which makes them Dlainly visible. The breaker height, H, , 

 and the depth of breaking, d, , defend unon a number of factors: 

 the steepness and direction of the waves in deer) water, the slope 

 and regularity of the bottom, the strength and direction of local 

 winds, and the number of v-'ave trains present. As yet no general 

 rules can be given, but the ratio H, /H appears to lie bet^'een one 



59 



