exerted on the grains by accelerations and decelerations of the fluid 

 particles in this flow situation. These forces are random in nature and this 

 randomness also is exhibited in associated sediment transport rates and 

 directions. In light of this, dimensional analysis techniques or other means 

 typically are used to obtain relationships and parameters that have empirical 

 coefficients to predict the point of incipient sediment motion. Surprisingly, 

 Madsen and Grant (1975) found that the Shields function for unidirectional 

 flows is also relatively reliable as a general criterion for threshold of 

 movement under irregular flows such as overpassing water waves. As a first- 

 order approximation, linear wave theory may be used to describe near-bottom 

 velocities. However, linear theory assumes purely oscillatory motion, which 

 implies no net sediment transport even if incipient (threshold) velocity 

 requirements are exceeded. It is well known that nonlinear effects are 

 introduced by wave asymmetries, bottom irregularities, and wave- induced mass 



>- 



ra 



1.00 r 



0.10 



0.01 



NO MOVEMENT 



_t i i i 1 1 1 1 



10 



100 



1000 



u. d 



Figure 2. Curve representing conditions of incipient motion 

 in unidirectional uniform flows 



11 



