SECT. 3] BEACH AND NEABSHORE PROCESSES 525 



circulation in the vertical plane, forwards at the water surface and backwards 

 below. The latter, backward drift below is likely to reduce or even reverse the 

 forward wave drift, but in the absence of controlled experiments it is not known 

 for sure whether the circulation due to wind effect is continuous or of a repeating 

 cellular type. 



(b) Under an imposed, surface-wind drag the water waves, being no longer 

 wholly self-propagating, have a different character. Considerable turbulence 

 develops from the water surface downwards, in addition to the turbulence due 

 to bed drag. The effect of this on the Longuet-Higgins bed-water drift attribu- 

 table to the waves cannot be predicted theoretically. Its experimental study, 

 in common with that of many other wind effects, awaits the construction of 

 suitable laboratory apparatus. 



7. Threshold of Bed Disturbance by Fluid Action 



A. Steady Unidirectional Flow 



The threshold at which cohesionless bed grains are just disturbed and set in 

 motion is usually assumed definable by the critical value of the mean distri- 

 buted stress, TO, exerted by the fluid flow on the bed surface. The critical value, 

 Tt, is that at which gravity and frictional forces holding the least firmly bedded 

 grains in place are just overcome by fluid forces. 



On this view, following the work of Shields (1936), the natural threshold 

 criterion is the ratio dt of the critical shear stress rt to the immersed weight, 

 represented by {ps —p)gD, of the topmost grain layer of the bed. dt thus has 

 the nature of a generalized friction coefficient which takes both grain size and 

 grain density into account. We have, therefore, 



dt = Ttl{ps-p)gD. (16) 



Under precisely similar conditions of grain size and bed packing, of bed 

 surface configuration, fluid turbulence and degree of steadiness of the flow, and 

 of the mode of application of the applied fluid forces to the individual exposed 

 grains, the threshold friction coefficient 9t would be expected to be a constant 

 number. 



For fully turbulent flow over flat beds of natural grains exceeding about 1 mm 

 in size, which do not spontaneously become rippled under continued flow over 

 them, the value of dt has been found, in fact, to be very nearly constant, 

 varying only between 0.04 and 0.06. In the case of beds of finer grains, the 

 ripples of which have already become fully developed by a previous flow, 9t is 

 found to increase with decreasing grain size, from 0.04 to 0.25 or more, owing 

 to the "form drag" exerted by the ripple features. 



The variations of 9t with grain size, calculated from Shields' experimental 

 results, are shown in Fig. 5 by curve A for grains of quartz density, ps = 2.65, and 

 by curve B for lighter grains, ps= 1.5. But Shields' results refer to initial move- 

 ment over beds which had been artificially smoothed out. For reasons explained 

 in Bagnold (1956), however, uniform grain movement over smooth beds of 



