244 



TRANSPOKTATION OF DEBKIS BY SUNNING WATEE. 



downstream faster than the current. They 

 are initially rhythmic, but their period is 

 unstable because their velocity of propagation 

 varies with their size. A wave with slight 

 advantage in size will overtake the one in 

 front of it, and then the two will unite, making 

 a wave with still higher velocity. Thus the 

 system tends, for a time at least, toward 

 reduction of the number of waves and increase 

 of the wave interval. As the waves grow by 

 composition, their fronts steepen and the 

 culminating phase is that of a "roll wave," or 

 bore. 1 It may be noted, in passing, that the 

 pulsations frequently observed in the overfall 

 of a dam are probably rhythms of this type. 



It may be assumed, at least tentatively, 

 that all the dominant rhythms observed in 

 straight conduits are initiated at the intake. 

 Those associated with low velocity and an 

 immobile bed appear to be stationary, but 

 with a mobile bed they develop dunes, and 

 they then travel downstream with the dunes. 

 Those associated with high velocity and an 

 immobile bed develop waves of translation 

 which travel downstream. With a mobile bed 

 antidunes are developed, and surface waves 

 travel with them upstream. It is possible 

 that the antidune waves coexist with the 

 waves of translation, and that the cycle of 

 intensity in the antidune phenomena results 

 from the interactions of the two systems. 



If there is warrant for the various correlations 

 above indicated, the phenomena developed by 

 our experiments in connection with modes of 

 debris transportation afford a basis of classifi- 

 cation for a considerable body of water 

 rhythms. What we have called the smooth 

 phase of traction marks a critical phase of 

 water flow separating two types which are 

 characterized by dominant rhythms, and the 

 two dominant rhythms are in some way anti- 

 thetic. The nature of their antithesis is not 

 known to me, nor is the character of either 

 rhythm; but it appears that the experimental 

 and analytic study of the rhythms constitutes 

 a field of research which is at the same time 

 promising and important. I assume that the 

 definite rhythms of water by which, when 

 debris is present, the dunes and antidunes are 

 caused are susceptible of analytic treatment, 



1 See Cornish, Vaughan, Progressive wfcves in rivers: Geog. Jour. 

 (London), vol. 29, pp. 23-31, 1907. 



and I believe that the experiment trough 

 affords the means of preliminary delineation 

 and ultimate verification. 



THE VERTICAL VELOCITY CURVE. 



No systematic study was made of the distri- 

 bution of velocities within the streams of the 

 laboratory, but incidentally, in connection with 

 several different minor inquiries, the vertical 

 distribution of velocities in the medial plane 

 was recorded; and it happens that some of 

 these records serve to illustrate the depend- 

 ence of that distribution the vertical velocity 

 curve on' certain conditions. The observa- 

 tions were made with the Pitot-Darcy gage. 



The first to be reported were made ia con- 

 nection with a comparison of the free outfall 

 (fig. 1, p. 19) and the contracted outfall (fig. 3, 



FIGURE 73. Modification of vertical velocity curve by approach to 

 outfall. 



p. 25). The trough used with free outfall had 

 smooth sides and bed, was 1 foot wide, and 

 was set level. The stream of water, 0.734 

 ft. 3 /sec., carried no debris. Its surface slope 

 gradually increased toward the outfall, and the 

 mean velocity increased with the fall of the 

 surface. Velocities were measured at three 

 points, respectively, 5.5 feet, 2.3 feet, and 0.8 

 foot from the outfall. Their curves, given in 

 figure 73, show that the acceleration as well as 

 the velocity increased as the outfall was ap- 

 proached, and that there was a coordinate 

 modification of the shape of the curve. In the 

 first curve it is evident, despite a discordance 

 among the determined points, that the level of 

 maximum velocity is somewhat above mid- 

 depth; in the second the maximum is near mid- 

 depth; and in the third it is below. The accel- 

 eration, for Avhich an integrated expression 

 appears in the horizontal space between curves, 



