0.5 



3.0 



1.0 1.5 2.0 2.5 

 Argument x 



Figure. Graph of the functions, sinh x 

 and x(tanh x) . 



For maximum water depth computation, the calculated [wH/2(5to)] is used as 

 the ordinate of the (sinh x) curve in the Figure to determine the value of the 

 argument x = (Zir d/L) . This permits finding the value of [(2tt d/L) tanh (2tt 

 d/L)] in the Figure. According to equation (7), the last value multiplied by 

 (g/(jo2) is the maximum water depth for sand motion, d„ 



max' 



3. Consideration of Other Physical Factors. 



The calculation procedure presented above is based on a review of available 

 laboratory results for sediment motion initiation by sinusoidal fluid flow over 

 a leveled horizontal bed of well-sorted sand. This data base does not reflect 

 effects of several physical factors potentially important in common situations, 

 such as poorly sorted sands, bed forms, mean bed slope, wave height, frequency 

 or direction spectrum, and any superimposed steady flow. Another possible limi- 

 tation is that the linear theory is used for calculating wave characteristics, 

 in particular, peak near-bottom fluid velocity. Some pertinent information on 

 these assumptions and omissions is presented below. 



a. Linear Wave Theory . Available information indicates that the linear 

 wave theory accurately gives near-bottom velocity if 



s-^ss: 



2d 3 



(8) 



