518 BAGNOLD [chap. 21 



The evidence so far available suggests that the ultimatel}' constant value of 

 K is n function of the scale of the flow in terms oi hjD, where h is the flow depth 

 and I) the mean grain diameter of the transported sediment ; and, further, 

 provided the gravity slope tan ^ is small compared to wjUg, K is independent 

 of the absolute value of D. Over the large range of scale from miniature labora- 

 tory streams to the Mississippi river, A'max apjDears to have values of the order 

 of I logio {hi I)). The reason for this apparent scale effect is not clear. The scale 

 of the turbulent eddies may be involved. 



D. Transport under Oscillating Water Motion due to Surface 



Waves 



From the generality of the reasoning leading to (9), it seems likely that the 

 mean rate, i, of to-and-fro transi^ort of sediment over the sea bed by a purely 

 oscillatory motion of the water close to the bed will also be found by experiment 

 to attain proportionality to the power co as given by (6). 



Since the mean rate,y, of the to-and-fro transport is equal to rnllo, where m 

 is the mean sediment mass supported over unit bed area and Uo is the mean 

 velocity of the sediment's to-and-fro motion, the immersed weight of the 

 supported sediment will be ijUo, which by (9) can be written T^'co/C/o. Since 

 the sediment is already supported by the wave action, no additional 

 tangential stress should be needed to produce a transport of sediment at 

 velocity Ue by a bed current of velocity Ue in any direction 6. Hence, assuming 

 as a reasonable approximation that UelUo'^Ueluo, where uq is the orbital 

 velocity measured at the same distance from the bed as Ue, the sediment 

 transport rate in the direction 6 should be given by 



ie = K'<o—. (10) 



Uo 



Before proceeding to discuss the property of surface waves in shallow water 

 of creating a bed-drift current of their own, it is convenient here to point out 

 a particular implication of relation (9) which appears to throw light on a 

 number of puzzling phenomena including turbidity currents. 



5. Auto- suspension of Sediment: Turbidity Currents, etc. 



The theoretical possibility of this phenomenon was briefly alluded to by 

 Bagnold (1956, p. 270). Since then factual evidence of its widespread existence 

 has emerged in the course of research carried out under the auspices of the U.S. 

 Geological Survey. 



Just as a sediment bed will transport itself in unlimited quantity as an 

 avalanche of bed load, Avithout any energy supply from the fluid, when the 

 gravity gradient, tan /S, becomes equal or exceeds the internal friction gradient, 



