transport currents. These effects disturb the equilibrium that would be 

 exhibited by the purely to -and- fro motion assumed by linear wave theory, and 

 result in a net transport of sediment. Additional discussion of this subject 

 may be found in numerous sources (Silvester 1974, Komar and Miller 1974, 

 Madsen and Grant 1975, Middleton and Southard 1978, Hales 1980, and Herbich et 

 al . 1984). For sediments subjected to wave and current action, the time 

 histories of lift and drag forces are much more complex and analysis is far 

 more difficult. In spite of the difficulties, numerous relationships have 

 been developed for critical velocities V c in oscillatory flows: 



Hallermeier _ fft , Y s . , , . s (7) 



(1981) v c ~ lB <— x > ST a g \ 



fufiii" <»«> '.■ ■ ^i^W-i) "»'*•» <8) 



Y 



Madsen and Grant .. 2 V B ^ /j. \ 



(1975) v c = V^ tan(4>,) 



u.d„ 

 + 0.66 for < g < 70 



co log u. (d/v)-0.06 



Yang ,.._. 



(1973) (io; 



— - = 2.05 for 7 < -^—2 



and the relationships of Komar and Miller (1974) 



= 0.21 (AjdJ 1/2 for d„ < 0.05 



pu max = n ■>^ tz /w 11/2 



{p e -p)gd q 



Komar and nn 



Miller (1974) V-L-IO 



= 0.46 tc (A„/dJ 1/4 for d„ > 0.05 



(p e -p) gd 



For the above , 



d g = median grain diameter, ft 



C D = drag coefficient 



12 



