otherwise, surface waves have a nonsinusoldal profile and a calculation using 

 linear wave theory may underestimate the actual peak near-bottom velocity. 

 Using the values of (d/L) and (d/E) found in determining critical conditions, 

 S can be conveniently calculated. If equation (8) is not satisfied, the cal- 

 culated critical conditions must be regarded with appropriate caution. If the 

 minimum wave height for sand motion in a given depth has been calculated, a 

 somewhat smaller wave height might actually induce motion; if the maximum water 

 depth for sand motion with a certain wave height has been calculated, sand 

 motion might actually occur in a somewhat greater water depth. 



b. Poorly Sorted Sand . If there is a wide range of grain sizes in a sedi- 

 ment sample, some evidence indicates that the effective grain size for consid- 

 eration of sediment movement is smaller than the median sediment diameter, D, 

 commonly taken to describe the sediment. No quantitative guidelines can be pre- 

 sented, but if the sand is judged to be poorly sorted (e.g., bimodal) , calcula- 

 tions using D for critical conditions should be regarded with the same caution 

 described above: the present procedure provides the minimum extent of bed 

 activity for the specified wave condition. 



c. Bed Forms . Sand motion initiation on a bed with previously fully grown 

 vortex ripples can be caused by a peak velocity that is about 50 percent of that 

 required on a level bed . Natural relict bed forms may not have this great an 

 effect on the critical fluid velocity for sand motion, but the prevalence of 

 relict bed forms in nature indicates that the present procedure provides the 

 minimum extent of bed activity. Bed forms also contribute to disorder in the 

 near-bottom boundary layer, which suggests that the motion criterion of equation 

 (2) , rather than equation (1) or (4) , provides the suitable minimum extent of 

 bed activity, 



d. Mean Bed Slope . A sloping bed can affect the process of motion initia- 

 tion through the component of grain weight along the bed. Available studies 

 support the accuracy of the present criterion for sand motion initiation on 

 plane slopes gentler than 1 on 15. On a steeper sand slope, available data 

 indicate a lower velocity than that given by the present criterion is required 

 for sand motion, so that the present procedure would provide the minimum extent 

 of bed activity. 



A sloping bed causes wave transformation that is more complicated than the 

 wavelength change included in the present procedure. Available information 

 supports linear theory results for a wave height change in shoaling on slopes 

 of 1 on 20 or gentler if 



^ < 30 (5) 



It is certainly consistent with the accuracy of the fundamental correlations 

 in equations (1) and (2) to ignore the usually small wave height changes given 

 by linear theory whenever 



^ > 0.075 (10) 



