■7 



SECT. 3] BEACH AND NEARSHORE PROCESSES 521 



For beds of fine sand or silt which become rippled, the length Di is some- 

 where between the ripple length and the jjarticle diameter. So a length of 1 cm 

 would not be far wrong as a rough estimate. 



To allow for the effect of the upper flow boundary, the number 0.03 on the 

 right of (13) could be increased to say 0.045 or 0.06. But an assumption has to 

 be made here that the concentration N remains sufficiently small for the dis- 

 persion of solids in the fluid to have no appreciable effect on its flow resistance. 

 If N exceeds, say, 1% (by volume), the flow resistance, and, therefore, the 

 number on the right, is likely to increase. 



The criterion (13) predicts that a turbidity current cannot continue to flow 

 indefinitely down a dechned bed under still water unless it has initially attained 

 a finite velocity u such that u sin /3 exceeds the fall velocity w of its solid 

 particles. It also predicts that for a given value of {sin ^ —wju) the "scale '''' 

 factor", NhlogiQlS.'IhjDi, must exceed a finite Hmiting value; for given 

 values of sin j8 and w, the scale factor should be a minimum when ivju = 

 2 sin ^/3. 



Further it suggests that, if the initiating event, e.g. an avalanche, results in 

 the value of the expression on the left exceeding the number on the right, the 

 flow might become unstable and might begin to "snow-ball". The excess power 

 might tend to increase as the current progresses by the entrainment of more 

 sediment from the bed, until ultimately a power balance is set up by a resulting 

 increase in u. 



The general idea seems sufficiently reasonable to provide a useful guide both 

 to what is physically possible in nature, and also to the design of laboratory 

 experiments whereby the jjhenomenon could be studied under controlled 

 conditions. 



For instance, suppose in nature a major avalanche down a steep continental 

 slope were to result initiaUy in a stationary ball of turbidity of height h ' con- 

 taining a mean concentration N' by volume of dispersed sohds of quartz 

 density ; and suppose that the excess hydrostatic pressure at the base were to 

 accelerate a current, of ultimate thickness A = 500 m and of concentration 

 iV = 0.01, to an ultimate speed ^ over an ocean floor sloping at 0.6" (sin ^ = 0.01). 

 Evaluation of (13) for flne sand {w<^u sin |8), taking the number on the right as 

 0.045, gives the speed, u, attainable to be 25 m/sec. If the entrained sediment 

 were such that w = ^u sin /8, u would be reduced by a factor l/\/3 to 14.5 m/sec, 

 for which w=lO cm/sec (grains of 1 mm diam.). 



The current might well, of course, drive still larger grains over the floor as 

 un-suspended "bed load". 



Acceleration of the current to these high speeds must, however, involve 

 considerable initial pressure heads. The excess height, h', of the original 

 turbidity must exceed u^l'2{ps -p)gN' . If ^ = 25 m/sec, h' must exceed 1900 m 

 for iV' = iV = 0.01, but N' might have a considerably larger temporary value 

 during the initial stage, while large solids were still falling out. 



The criterion (13) suggests that a self- maintaining turbidity current of the 

 kind described should be easily reproducible on a laboratory scale on somewhat 



