522 BAONOLD [chap. 21 



exaggerated slopes, using sediment which has an appreciable fall velocity. An 

 important requirement here would be that the mean eddy velocities of the 

 turbulence sufficiently exceed the fall velocity w, so that fully developed 

 suspension is ensured. 'J'hus, indejjendently of (13), the current velocity m 

 created by the initial disturbance might have to be 20 to 30 times iv. 



The experimental verification of (13) would be of considerable interest. In 

 particular one would like to know the precise value to be given to the number 

 on the right when an upper-fiuid-flow boundary exists, and also the limiting 

 concentration N at which this number begins to increase appreciably. 



Auto-suspension may also occur when the fresh water of a sediment-laden 

 river outflows over the heavier sea-water (sometimes for distances of several 

 hinidred kilometres). By existing theories suspension of sediment by turbulent 

 flow cannot be maintained unless there exists a continuous increase in con- 

 centration downwards to a sohd flow boundary. In this case there is no such 

 boundary, and a downward increase in concentration would seem to be im- 

 possible. So the suspended sediment would be expected to fall out at the same 

 rate as if the outflow of the overlying fresh water were non-turbulent. 



But auto-suspension allows of the retention of sediment whose fall velocity 

 IV is less than u tan /8 provided the flow remains turbulent. Here u is the flow 

 velocity of the fresh water over the salt water and tan 13 is the residual flow 

 gradient of the river. Accordingly, the turbidity should disappear somewhat 

 abruptly, as it is observed to do when the Reynolds Number, uhjv, of the flow 

 falls below, say, 2500 and the turbulence dies out. For observed end-thicknesses 

 of the fresh turbid layer of 15 cm, its velocity u of flow should be about 1.6 cm/ 

 sec. Assuming a residual surface water gradient of 10~6, the critical fall velocity 

 w would be 1.6 x 10-^ cm/sec, and particles 0.1 pi in size would persist at the 

 water surface until the final cessation of turbulence. 



Measurements of the depths of the fresh-water flow, of its velocity relative to 

 the underlying sea-water, and of the sediment size and concentration at varied 

 seaward distances from the river mouth w^ould be of much interest. 



FinaUy, auto-suspension may account for the existence of a lower limit to 

 the size of shore sand. Though the beds of estuaries often consist of fine silts 

 and muds the sands of open sea shores rarely contain grains less than 0.15 mm 

 in size. Taking | knot or 25 cm/sec as a fair average for the onshore and off- 

 shore currents due to waves, and 3° (tan /3 = 0.05) as a fair average bed slope 

 offshore of the breaker zone, all sediment grains whose fall velocity is less than 

 25 X 0.05 = 1.25 cm/sec shoidd tend to become uniformly dispersed in the turbu- 

 lent water of the breaker zone, and, therefore, to diffuse outwards into deeper 

 water. From Fig. 1 the grain size corresponding to this fall velocity is in fact 

 0.15 mm. 



6. Wave Drift 



Wave theory considers water motion relative either to still water "elsewhere" 

 or to axes stationary with regard to the mean position of all the water particles 



