232 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



dune transformations. 1 A similar remodeling 

 was observed by Partiot in the Loire. 2 Hider 

 estimated the whole movement in dunes as 

 14,800 cubic yards in 24 hours, which corres- 

 ponds to 2.2 per cent of the average suspended 

 load reported by Humphreys and Abbot; but 

 his judgment was that the entire movement of 

 debris along the bed was at least ten times as 

 great as the movement in dunes. 



As a generalization from extensive observa- 

 tions of dunes in the river Loire, Sainjon formu- 

 lates their rate of advance when the material is 

 sand as a function of surface velocity, V s . In 

 his equation 3 



Advance = 0.000 13 ( I 7 , 2 - 0.11) 



the units are metric. Substituting feet for 

 meters, we have 



Advance = 0.00004 ( F s 2 - 1.18) 



The associated average height of dune crests 4 

 is 0.77 meter, or 2.54 feet. As the mean height 

 of a dune is approximately one-half the height 

 of its crest, we may multiply the rate of advance 

 by 2.54/2 and obtain 



0.00005 ( T7-1.18) 



as an expression for the Loire's load of sand 

 carried in dunes, for each foot of channel width 

 occupied by. dunes. In a later discussion by 

 Lechalas (see p. 193) it is shown that Sainjon's 

 formula does not apply to surface velocities 

 above 3.3 ft. /sec., the rate of dune advance being 

 then checked because part of the sand escapes 

 into the body of the current and is not added 

 to the downstream faces of the dunes; but the 

 observations on dunes constitute the quanti- 

 tative basis of the formulation of debris trans- 

 portation by Lechalas, of which an account is 

 given in Chapter X. 



In this connection mention may be made of 

 moving sand bodies of a different order of mag- 

 nitude and probably of a different type. They 

 are greater than the dunes of the same stream 

 and are coordinate in size with the bars sepa- 

 rating deeps but are distinguished from the 



i Mississippi River Comm. Kept, for 1882, pp. 80-88. Observations 

 by W. H. Powless, made at a different place and in another year, are o( 

 the same tenor. See idem for 1881, pp. 66-120. 



> Annales des ponts et chaussees, M&n., Sth ser., vol. 1, p. 270, 1871. 



a Quoted, with some of the data, by Partiot, idem, pp. 271-273. The 

 coefficient is there erroneously given as 0.0013. 



< Given by Lechalas in the same volume, pp. 387-388. 



bars by their migration downstream. In some 

 of the "regularized " streams of Europe-, where 

 the main channel is artificially restricted to 

 curves of large radius, they are developed in 

 systematic alternation at the two sides, and the 

 thalweg winds between them. 5 In the Missis- 

 sippi they sometimes appear in the reaches. 

 Their progress downstream is accomplished by 

 deposition on forward slopes and erosion of rear 

 slopes, but the forward slopes are not steep, like 

 those of dunes, and their material is not wholly 

 deri ved from the traction al load. Blasius 8 re- 

 gards them as essentially dunes, correlating 

 them specifically with dunes of reticulated pat- 

 tern. My own view, not necessarily inconsist- 

 ent with his, connects them with the fixed bars 

 separating the deeps of a meandering stream. 

 A free stream does not tolerate a straight chan- 

 nel. If a straight channel of moderate width be 

 given to a stream, the current swings rhyth- 

 mically to right and left, and if the banks 

 yield it develops meanders. The meanders 

 then migrate, according to laws of their own, 

 and the bars are fixed in relation to the mean- 

 ders. If the banks do not yield, the system of 

 shoals and deeps established by the swinging 

 current migrates slowly downstream. It is 

 evident that the migration of these shoals is 

 one of the factors and may be an important 

 factor in the work of transportation ; and also 

 that every measurement of the migration of a 

 shoal is a partial measurement of load. 



Pilots of Mississippi steamboats observe 

 that the bars at crossings are built up by floods, 

 and such changes have been measured by 

 engineers. The generalization has sometimes 

 been made that deposition is a specific function 

 of floods, but a more satisfactory interpretation 

 is given by McMath, 7 who maintains that the 

 rising river scours from the deeps to deposit on 

 the shoals, and the falling river scours from 

 the shoals to deposit in the deeps. The 

 transfers are the joint work of traction and 

 suspension. As such changes of the stream 

 bed are measurable they afford quantitative 

 data as to load, and it was from their observa- 

 tion that Hider, as previously quoted, inferred 

 that the dune movement in the Mississippi 

 includes but a small fraction of the tractional 

 load. 



t Engels, H., Zeitschr. Bauwesen, vol. 55, pp. 604-680, 1905. 



s Idem, vol. CO, pp. 4(3-472, 1910. 



i Mississippi River Comm. Kept, for 18X1, p. 252. 



