From (a) above the maximum horizontal distance 2A is 0.96 meter; 

 therefore, the ratio 2A/L is 



2A _ 0.96 _ 



IT " TzTil- °-°^ 



(d) Using the relation C = Vgd (Eq. 2-9) to determine the shallow-water 

 wave speed 



nd 



C =-^9.8 (0.6) = 2.42 meters (7.96 feet) per seco 



From (b) above, the maximum horizontal velocity ^mnx is 0.61 meter per 

 second. Therefore the ratio ^^^rnax^ ^ ^^ 



max 0.61 



2.42 



= 0.25 



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



Although small-amplitude theory gives a fair understanding of many wave- 

 related phenomena, there are important phenomena that it does not predict. 

 Observation and a more complete analysis of wave motion show that particle 

 orbits are not closed. Instead, the water particles advance a little in the 

 direction of the vave motion each time a wave passes. The rate of this 

 advance is called the mass transport velooity; (Ch. 2, Sec. II, 5, c). This 

 velocity becomes important for sediment transport, especially for sediment 

 suspended above ripples seavard of the breaker. 



For conditions evaluated at the bottom (z = -d) , the maximum bottom 



velocity, ^\nax(-d') Siven by equation (2-13) determines the average bottom 

 mass transport velocity \x,j^ obtained from equation (2-55), according to the 

 equation 



where C is the wave speed given by equation (2-3). Equation (2-55), and 

 thus equation (4-18), does not include allowance for return flow which must be 

 present to balance the mass transported in the direction of wave travel. In 

 addition, the actual distribution of the time-averaged net velocity depends 

 sensitively on such external factors as bottom characteristics, temperature 

 distribution, and wind velocity (Mei, Liu, and Carter, 1972). Most obser- 

 vations show the time-averaged net velocity near the bottom is directed toward 

 the breaker region from both sides. (See Inman and Quinn (1952) for field 

 measurements in surf zone; Galvin and Eagleson (1965) for laboratory 

 observations; and Mei, Liu and Carter (1972, p. 220) for comprehensive 

 discussion.) However, both field and laboratory observations have shown that 

 wind-induced bottom currents may be great enough to reverse the direction of 

 the shoreward time-averaged wave-induced velocity at the bottom when there are 

 strong onshore winds (Cook and Gorsline, 1972; Kraai, 1969). 



4-48 



