passes. The rate of this advance is the mass transport vetoaity; (Equa- 

 tion 2-55, Section 2.253). This velocity becomes important for sediment 

 transport, especially for sediment suspended above ripples seaward of the 

 breaker. 



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

 velocity, umoxr. j') . given by Equation 2-13 determines the average bottom 

 mass transport velocity, u(_j). obtained from Equation 2-55, according to 

 the equation 



("wax/ J)) 

 "(-d)='-^' . (4-12) 



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

 thus Equation 4-12, 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 character- 

 istics, temperature distribution, and wind velocity. (Mei, Liu, and Carter, 

 1972.) Most observations 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 Eagle- 

 son, (1965) for laboratory observations; and Mei, Liu and Carter (1972, 

 p. 220), for comprehensive discussion.) However, both field and labora- 

 tory 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; and Kraai, 1969.) 



4.42 FLUID MOTION IN BREAKING WAVES . 



During most of the wave cycle in shallow water, the particle velo- 

 city is approximately horizontal and constant over the depth, although 

 right at breaking there are significant vertical velocities as the water 

 is drawn up into the crest of the breaker. The maximum particle velocity 

 under a breaking wave is approximated by solitary wave theory (Equation 

 2-66) to be 



Hmax = '^ = v/g (H + d)' , (4-13) 



where (H+d) is the distance measured from crest of the breaker to the 

 bottom. 



Fluid motions at breaking cause most of the sediment transport in 

 the littoral zone, because the bottom velocities and turbulence at break- 

 ing suspend more bottom sediment. This suspended sediment can then be 

 transported by currents in the surf zone whose velocities are normally 

 too low to move sediment at rest on the bottom. 



Tlie mode of breaking may vary significantly from spilling to plung- 

 ing to collapsing to surging, as the beach slope increases or the wave 



4-42 



