Critical Depths for Incipient Sediment Motion 



8. In addition to critical velocity, it is often desirable to calculate 

 depths at which sediment transport occurs for oscillatory flows. Several 

 empirical formulas that have been used successfully to calculate critical 

 water depths for sand motion can be summarized in the following form: 



s—terK^u 



(12) 



In the above , 



H = deepwater wave height, ft 



L = deepwater wave length, ft 



a crit = empirically obtained coefficient for critical water depth calculation 



d g = median grain diameter of sediment, ft 



r\ = empirically obtained exponent for critical water depth calculations 



h c = critical water depth, ft 



H c = critical wave height, ft 



Table 1 (after Herbich et al . 1984) provides values of a orit and r\ as 

 empirically obtained by several researchers. 



Table 1 



Comparison of Values of a crit and r\ for Use in Equation 12 



Parameter 



Sato and 

 Kishi (1954) 



Kurihara et 

 al. (1956) 



Ishihara & 

 Sawaragi (1962) 



Sato, et 

 al. (1963) 



V 



1/2 



1/2 



1/4 



1/3 



1/3 



"crit 



10.2 



1.56-2.44 



0.171 



0.565 



1.35 



Type of 

 movement 



General 

 movement 



Incipient 

 movement 



Incipient 

 movement 



Surface 



layer 

 movement 



Completely 



active 

 movement 



Differences among the above values most likely are attributed to the various 

 criteria used by each researcher to establish critical conditions for sediment 

 transport. For example, Sato and Kishi used well-established general bottom 

 motion as their criterion, while Kurihara et al . and Ishihara and Sawaragi 



14 



