512 BAGNOLD [chap. 21 



(vi) Hence, in all cases, continued steady movement of sediment over the 

 bed recjuires that however much or httle the moving grains are dispersed from 

 one anotlier, a normal disjjersive stress [{ps —p)lps]gm cos /3 must be main- 

 tained across every plane of shear in order that the immersed sediment weight 

 may remain supported. This must also be true, on the average, in the case of 

 oscillatory motion due to the passage of sin-face water waves. 



Across the shear plane of the bed surface this stress must, over a representa- 

 tive period of time, have a mean value identical with that existing when the 

 whole sediment load is settled stationary upon the bed. 



The reality of this normal dis])ersive stress acting between the moving 

 sediment grains and the bed boundary is logically indisputable, as are also the 

 inference (a) that this stress must result from the dynamics of the shearing 

 either of the fluid or of the sediment grains or of both, and (b) that the mech- 

 anism of sediment transport cannot be quantitatively miderstood until the 

 dynamics of the combined shearing are understood. 



It is clear from observational evidence of a qualitative kind that the normal 

 stress which supports the moving sediment load must arise from two different 

 dynamical mechanisms. For, though it is inescapable that fine sediment grains 

 in low concentration are maintained suspended by dynamic fluid forces exerted 

 by random eddies of turbulence, sediment is also maintained in a statistically 

 dispersed state as "bed load" under conditions where fluid turbulence is either 

 absent altogether or incapable of exerting the necessary forces on large grains. 



Far too little is understood at present about the mechanism of fluid turbu- 

 lence to allow of any theoretical prediction as to the load of suspended sediment 

 which a given flow can carry. But enough light has been thrown on the bed-load 

 mechanism by a study (Bagnold, 1954) of the collision dynamics of sheared 

 grain dispersions within fluids to suggest that the most useful a])proach to 

 the sediment-transport problem is likely to be from the direction of energetics 

 rather than that of dynamics. 



4. Transport Rate and Fluid "Power" 



The general background of the new approach to sediment-transport problems 

 outlined in this and the following sections has been discussed in a general way 

 in a paper already publishcfl (Bagnold, 1956). The results are introduced here 

 with special reference to marine conditions, together with summarized versions 

 of further developments since 1956, a more ample discussion of which it is 

 hoped will shortly be published as a U.S. Geological Survey Professional 

 Paper in the series 282. 



A. Work Done in Transporting a Bed Load 



Repeated coUisions between the solid grains, as they are sheared over one 

 another and over the bed grains, must necessarily create components of grain 

 momenta both normal and parallel to the planes of shear (Fig. 2b). The diffu- 

 sion of the normal components from grain to grain constitutes a normal stress 



