220 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



FEATURES CONNECTED WITH CURVATURE OF 

 CHANNEL. 



As nearly all the laboratory experiments were 

 performed with straight channels, and as all 

 natural channels are more or less curved, the 

 features resulting from curvature constitute 

 differences of which account must be taken in 

 applying laboratory results. Some of these 

 differences have been mentioned in connection 

 with the short series of experiments with 

 curved and bent channels, but a fuller account 

 is desirable. 



In a straight channel the current is swifter 

 near the middle than near the sides and is 

 swifter above mid-depth than below. On 

 arriving at a bend the whole stream resists 

 change of course, but the resistance is more 

 effective for the swifter parts of the stream than 

 for the slower. The upper central part is de- 

 flected least and projects itself against the outer 

 bank. In so doing it displaces the slow-flowing 

 water previously near that bank, and that water 

 descends obliquely. The descending water dis- 

 places in turn the slow-flowing lower water, 

 which is crowded toward the inner bank, while 

 the water previously near that bank moves 

 toward the middle as an upper layer. One 

 general result is a twisting movement, the up- 

 per parts of the current tending toward the 

 outer bank and the lower toward the inner. 1 

 Another result is that the swiftest current is no 

 longer medial, but is near the outer or concave 

 bank. Connected with these two is a gradation 

 of velocities across the bottom, the greater ve- 

 locities being near the outer bank. The bed 

 velocities near the outer bank are not only 

 much greater than those near the inner bank, 

 but they are greater than any bed velocities in 

 a relatively straight part of the stream. They 

 have therefore greater capacity for traction, 

 and by increasing the tractional load they erode 

 until an equilibrium is attained. On the other 

 hand, the currents which, crossing the bed ob- 

 liquely, approach the inner bank are slackening 

 currents, and they deposit what they can no 

 longer carry. 



It results that the cross section on a curve 

 is asymmetric, the greatest depth being near 



i The system of movements here described has been observed by 

 many students of rivers. They were demonstrated by the aid of a model 

 channel by J. Thomson, in connection with an explanation which dif- 

 fers somewhat from that of the present text. See Roy. Soc. London 

 Proc., pp. 5-8, 1876, and 35C-357, 1877; also Inst. Mech. ICng. Proc., pp. 

 455-400, 1879. 



the outer bank. As the winding stream 

 changes the direction of its curvature from one 

 side to the other, the twisting system of current 

 filaments is reversed, and with it the system of 

 depths, but the process of change includes a 

 phase with more equable distribution of veloci- 

 ties, and this phase produces a shoal separating 

 the two deeps. The shoal does not cross the 

 channel in a direction at right angles to its 

 sides but is somewhat oblique in position, 

 tending to run from the inner bank of one 

 curve to the inner bank of the other. In 

 meandering streams it is usually narrow and 

 is appropriately called a bar. In direct alluvial 

 streams, where bends are apt to be separated 

 by long, nearly straight reaches, it is usually 

 broad and may for a distance occupy the 

 entire width of the channel. In navigated 

 rivers the locality of the bar is usually called a 

 crossing, being the place where the thalweg, 

 the line of strongest current, and the route of 

 travel cross from side to side; and the name is 

 often applied also to the bar itself. 



The twisting current attacks the outer bank, 

 being swifter at contact with that bank than 

 in any other part of the wetted perimeter. If 

 the bank consists of alluvium there is erosion, 

 the amount being determined in part by 

 resistances arising from roots, or adhesion of 

 alluvial particles, or incipient cementation; 

 and the eroded material, so far as it joins the 

 bed load, helps to satisfy the bed current and 

 limit downward erosion. In alluvial streams 

 the erosion from concave banks offsets the 

 deposition under convex banks, so that the 

 channel may gradually shift its position without 

 change of sectional area. 



The sectional area may be either greater or 

 less at a curve than on a reach, but the differ- 

 ences are normally 1 of small amount. There- 

 fore the mean velocity does not vary greatly. 

 The current in a curved channel, as compared 

 to that in a straight channel, is characterized 

 by diversity. Its bed velocities are both 

 higher and lower, and the same is true of 

 velocities along the banks. This diversity is 

 favorable to traction, because capacity for 

 traction varies with a high power of velocity; 

 but the advantage to traction is partly offset 

 by the fact that increase of velocity affects a 

 smaller portion of the wetted perimeter than 



'That is to say, they are of small amount when the system of depths 

 is adjusted to the discharge, as explained on a later page. 



