526 



BAGNOLD 



[chap. 21 



grains less than about 0.7 mm in size is associated with an inherent instabihty 

 owing to which the bed surface becomes rippled iiiuh r any continuing move- 

 ment. 



'I'liougli the i)rimary rii)i)Ie system thus created offers but little form drag, 

 it becomes increasingly lial)le to a second instability as the grain size is further 

 reduced. This second instability is associated with the interaction between 

 the raised ripple features and the scouring effects of the vorticity the raised 

 boundary form creates. It results in the formation of another ripple system 

 which offers considerable form drag. 



Though much more controlled experiment is necessary, it seems on existing 

 evidence that the threshold value of 6t, if measured after the secondary ripple 



or 



or 



10-2 



GRAIN DIAMETER in mm 



Fig. 5. Variations of the threshold friction coefficient 9t with grain size. (After Shields, 

 1936.) 



system has been allowed to develop fully under a previous flow, is approxi- 

 mately as shown by curve C. The factual evidence does not, however, extend 

 to beds of grains less than 0.2 mm. 



Owing to the sudden jump in the value of 0^ due to the secondary in- 

 stability, it is possible for two very different values to be obtained for the same 

 experimental sand, and this has undoubtedly led to considerable misunder- 

 standings in the past. 



It is noteworthy that the sudden transformation of a primary ripple system 

 into another system, which is clearly associated with the effects of local vorti- 

 city, has also been observed under the oscillating water motion due to surface 

 waves. 



It is also noteworthy that few if any experiments have been done on the 

 behaviour of bed grains of controlled size less than 0.2 mm either under steady 

 or oscillating conditions. Nor have the effects of varying either the distribution 

 of grain sizes or the depth of the flow on the threshold by bed movement 

 received the systematic study they deserve. 



