SECT. 3] BEACH AND NEARSHORE PROCESSES 519 



tan (f), so we should expect a suspended load to transport itself to an unlimited 

 extent when tan ^ exceeds the gradient ivjUs. 



The power expended by the fluid in supporting the suspended sediment load 

 is isWJUs. The power expended by gravity directly on the sediment is ig tan j8. 

 But the latter power is transmitted from the sediment grains to the fluid 

 surrounding them. Hence, if tan jS exceeds wjUs, the suspended sediment, owing 

 to its excess density, has the effect of j)ushing the fluid along instead of vice 

 versa. A vessel floating down a river has no excess density so it cannot push 

 the water along. 



This concept appears first to have been suggested by Knapp (1938, p. 501), 

 but its significance was overlooked and it was arrived at independently by 

 Bagnold (1956, 1962). The reality of the effect, which is confined to conditions 

 of turbulent fluid flow, should be manifested in the foUowing ways: 



(a) The transport rate, ig, of such sediment grains as have fall velocities w 

 less that Us tan ^ should be unlimited, except by availability of material, and, 

 ultimately, at very high concentrations, by the suppression of fluid turbulence 

 as the apparent viscosity is increased. 



(b) Contrary to existing theories of turbident suspension, all of which 

 l^ostulate a continuous increase in concentration downwards towards the bed 

 boundary, sediment grains for which w<Us tan ^ should tend to distribute 

 themselves uniformly throughout the fluid. 



(c) Grains for which w just exceeds Us tan ^ should be found in streams in 

 greatest concentration where Us is greatest, i.e. in the upper fluid layers where 

 the fluid velocity u is greatest. 



AU these manifestations have actually been observed. Extremely large 

 sediment-transport rates have on occasion been measured in rivers. But, as 

 far as the available data have been analysed, the mean sediment size is in every 

 case that for which the fall velocity w is less than Us tan ^ (Us being measured 

 approximately as the mean flow velocity, u, of the river). It is weU known to 

 hydraulic engineers that fine silt carried in suspension by water streams does 

 not tend to concentrate towards the bed, but is distributed uniformly through- 

 out the flow. The results of sediment samphng in rivers frequently disclose the 

 anomaly that although the overall concentration of suspended solids increases 

 downwards towards the bed the concentration of fine suspended grains 

 diminishes downwards towards the bed instead of increasing as conventional 

 theory requires. 



The evidence for auto-suspension ajjpears sufficiently strong to justify 

 applying the reasoning which predicted it to the problem of turbidity currents 

 along the sea bed. 



Consider, from the viewpoint of energetics, the conditions necessary for the 

 self-maintenance of a turbidity current of uniform thickness h flowing over a 

 gravity bed inclined downwards at an angle ^ (Fig. 4). Let the concentration, 

 N, of solid grains of density ps and having a fall velocity w be supposed uniform 

 and let the current velocity of both solids and liquids be u. 



The immersed load weight perpendicularly over unit bed area is {ps —p)gNh ; 



