of the breaker crest. Since it is this wave-induced water particle motion 

 that causes the sediment to move, it is useful to know the length of the 

 elliptical path traveled by the water particles and the maximum velocity 

 and acceleration attained during this orbit. 



The basic equations for water-wave motion before breaking are dis- 

 cussed in Chapter 2. Quantitative estimates of water motion are possible 

 from small -amplitude wave theory (Section 2.23), even near breaking where 

 assiomptions of the theory are not valid. (Dean, 1970; Eagleson, 1956.) 

 Equations 2-13 and 2-14, in Section 2.234 give the fluid-particle velocity 

 components u, w in a wave where small -amplitude theory is applicable. 

 (See Figure 2-3 for relation to wave phase and water particle accelera- 

 tion.) 



For sediment transport, the conditions of most interest are those 

 when the wave is in shallow water. For this condition, and making the 

 small-amplitude assumption, the horizontal length 2A, of the path moved 

 by the water particle as a wave passes in shallow water is approximately 



HT^gd 

 2A = -^^^ , C4-10) 



and the maximum horizontal water velocity is 



2d 



"^max = -TTT- ' (4-11) 



The term under the radical is the wave speed in shallow water. 

 ************** EXAMPLE PROBLEM *************** 



GIVEN : A wave 1 foot high with a period of 5 seconds is progressing shore- 

 ward in a depth of 2 feet. 



FIND ; 



(a) Calculate the maximum horizontal distance 2A the water particle 

 moves during the passing of a wave. 



(b) Determine the maximum horizontal velocity ^cuc °^ ^ water 

 particle. 



(c) Compare the maximum horizontal distance 2A with the wavelength 

 in the 2- foot depth. 



(d) Compare the maximum horizontal velocity ^cuc» with the wave 

 speed, C. 



4-40 



