d < 20 meters (66 feet), so the slope extends a sufficient distance offshore 

 to trap waves. From Figure 2-70 



Ym 



= 17 



Y = 17(2.0/0.03 = 1133 m (3,718 ft) 



For a long, relatively straight reach of coastline (greater than 1133 meters 

 long in this example), further investigation is needed to determine the 

 effects of trapped wave energy. 



*************************************** 



VI. BREAKING WAVES 



1 . Deep Water. 



The maximum height of a wave traveling in deep water is limited by a max- 

 imum wave steepness for which the waveform can remain stable. Waves reaching 

 the limiting steepness will begin to break and in so doing will dissipate a 

 part of their energy. Based on theoretical considerations, Michell (1893) 

 found the limiting steepness to be given by 



H 

 o 1 



— = 0.142 ^ - 

 ij / 



o 



(2-89) 



which occurs when the crest angle as shown in Figure 2-71 is 120°. This 

 limiting steepness occurs when the water particle velocity at the wave crest 

 just equals the wave celerity; a further increase in steepness would result in 

 particle velocities at the wave crest greater than the wave celerity and, con- 

 sequently, instability. 



Limiting steepness -p- = 0.142 



Figure 2-71. Wave of limiting steepness in deep water. 



2. Shoaling Water . 



When a wave moves into shoaling water, the limiting steepness which it 

 can attain decreases, being a function of both the relative depth d/L and 

 the beach slope m, perpendicular to the direction of wave advance. A wave 

 of given deepwater characteristics will move toward a shore until the water 



2-129 



