case some caution is warranted with regard to its applicability and its 

 accuracy. In developing the various relationships it was necessary to 

 simplify the physical model by making certain assumptions. Unless these 

 assumptions are still valid under the prototype conditions the method may 

 need modification. 



The basic assumption which practically governs the entire study was 

 that the amplitude of the surface wave was small (kH « 1); this permitted 

 the linearization of the equation of motion in the free stream. A second 

 assumption, but of lesser importance was that the depth of the water d was 

 rather large and uniform (small bottom slope.) 



We wish to emphasize at this point that the proposed method is only 

 meant to predict the motion of the bed material' within the bed layer. 

 Consequently it is not applicable in regions where the mixing is violent 

 and where considerable amount of sediment is being carried in suspension 

 as for instance near the surf zone and onshore. 



Another point that calls for attention is that the criterion of 

 instability of the boundary layer is not well defined. As stated in more 

 detail in Appendix A, there is some uncertainty regarding the slope of 

 the empirical curve serving as the criterion of instability in the region 



— < 6 x 10 ft . (Figure 1). Until this uncertainty is removed, it will 

 v 



be advisable in this region to use the line with the steeper slope pro- 

 posed by Manohar . 



The accuracy of the results, as one would expect, depends entirely 

 upon the quality of the approximations made in the course of developing 

 the various relationships. We shall examine these approximations of the 

 procedure step by step and make suggestions regarding their possible 

 improvement . 



a. This step deals only with the applicability of the method and 

 was covered already in the discussion above. 



b. The velocity distribution in the boundary layer was determined 

 experimentally in a flume under conditions similar but not identical to 

 those of the prototype. The error introduced this way cannot be very 

 significant and in fact it can be absorbed by the effect of the approxi- 

 mation made in the subsequent step. 



c. The value of Y was calculated from the velocity profile at a 

 distance y = .35D. This distance was so chosen because it has been proven 

 correct in dealing with steady mean flows; yet there is no proof that it 

 holds true in the case of an oscillatory mean flow also. The accuracy of 

 the method may be improved by determining the distance at which ¥ should 

 be calculated more precisely. 



27 



