248 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



the depth. The level of maximum velocity 

 thus has the same relation to side resistance as 

 to depth; it sometimes rises and sometimes 

 falls when side resistance is increased. While 

 a probability exists that side resistance influ- 

 ences the position of the maximum, the nature 

 of its influence is not shown by the observations 

 under consideration. 



Discharge and slope, or the energy factors 

 which they help to measure, urge the water 

 forward, and their influence is applied to the 

 whole stream. Bed resistance holds the stream 

 back but is applied to its base only. The 

 obvious tendency of these forces is to make the 

 upper part of the stream move faster than the 

 lower and produce a velocity curve with maxi- 

 mum at the water surface. This tendency is 

 opposed by some other factor, unknown, which 

 tends to depress the level of the maximum. 

 Whatever that other factor may be, it loses in 

 relative importance when discharge, slope, or 

 bed resistance is increased. 



A noteworthy feature of the curves is a 

 tendency to change in character near the bed. 

 The observations are not so precise nor so full 

 as to afford a distinct characterization of the 

 change, but there can be little question of its 

 existence. It would appear that the peculiar 

 conditions near the bed give great local impor- 

 tance to some factor of velocity control which 

 is elsewhere of minor importance. Attention 

 may also be directed to the fact that none of 

 the curves resembles an ordinary parabola 

 with horizontal axis. Had these been the 

 vertical velocity curves to which mathematical 

 formulas were first fitted, the equation of the 

 parabola would not have been used. 



The statement, above, that the factor 

 tending to depress the level of maximum 

 velocity below the water surface is unknown 

 is perhaps rash, for several theories as to its 

 nature have been advanced with confidence. 

 To put the matter more cautiously it has 

 seemed to me that each theory of which I have 

 read was effectually disposed of by the discus- 

 sion which it aroused. However that may be, 

 there is certainly room for another suggestion, 

 and this I proceed to offer. 



Reynolds * arranged an experiment in which 

 a liquid was made to flow over another denser 

 liquid, the two being immiscible. Below a cer- 



i Roy. Soc. London Philos. Trans., vol. 174, pp. 943-944, 1883. 



tain velocity the surface of contact was smooth, 

 but above the critical velocity the surface was 

 occupied by a system of equal waves, which 

 moved in the direction of flow but more slowly. 

 With miscible liquids, or with two bodies of 

 identical liquid, the waves are replaced by vor- 

 tices. Under some conditions the vortices are 

 as regularly spaced as the waves, but usually 

 they are less regular, and various complications 

 arise. The development of such vortices may 

 readily be watched on a river surface wherever 

 adjacent parts move with quite different veloci- 

 ties or move in opposite directions. Such vor- 

 tices have vertical axes, and their direction of 

 rotation is determined by the differential mo- 

 tion of the adjacent currents. If we conceive 

 the water of a vortex as a body between parallel 

 and opposed currents, then its direction of rota- 

 tion is due to a mechanical couple contributed 

 by the currents. 



Transferring attention to the longitudinal 

 vertical section of R stream, we find ft couple of 



FIGURE S3. Ideal longitudinal section of a stream, illustrating hypothe- 

 sis to account for the subsurface position of the level of maximum 

 velocity. 



which one element is the general forward move- 

 ment of the current and the other is the bed 

 resistance. These tend to produce and main- 

 tain vortices with horizontal axes transverse 

 to the channel and with forward rotation that 

 is, with the rotation of a wheel rolling forward in 

 the direction of flow. To visualize these fea- 

 t ures, figure 83 gives an ideal section of a stream, 

 with flow from left to right, and the ovals A, B, C 

 represent a system of forward-rolling vortices. 

 The arrows within an oval show direction of 

 rotation, and it is important to recognize that 

 the motions they indicate are referred to the 

 center of the vortex, or to the vortex as a 

 whole, and not to the fixed bed of the channel. 

 With reference to the bed all parts of the vortex 

 are moving toward the right, the lower part 

 merely moving slower than the upper. 



The tendency of vortices toward circular 

 forms leaves certain tracts of the section unoc- 

 cupied by the system of vortices. Consider the 

 tract D, bounded below by the bed and above 



