538 INMAN AND BAGNOLD [CHAP. 21 



bed transport velocity Ub and then backwards through the body of the ripple 

 at the much slower speed of the latters advance. 



Assmuing the ripple cross-section to be antisymmetrical about its mid- 

 plane the mean thickness of the sediment comi)osing it is 77/2, where 17 is the 

 whole height of the ripple from crest to trough. If D is the mean grain diameter 

 there will be r]l2D layers of stationary grains within the ripple at any moment. 

 If b is the number of eroded grain layers in motion at the speed Ub, the average 

 migration sjieed, Ug, will be 



Ug = Ub{2bDlr)). (19) 



It is not easy to measure the number b of moving grain layers. Observed 

 from above, the stationary bed grains become indistinct when b=\ and are 

 in\'isible when b exceeds 2. Thus a rough estimate can be obtained from 

 observation. 



It is instructive to compare the average speed of migration as estimated 

 from the above discussion and from the ideas of the preceding sections with 

 the actual speed as measured on the sea bed under conditions of wave motion. 

 Inman and Chamberlain (1959) re-deposited in situ a sample of about 1 kg of 

 sea-bed sand after its grains had been irradiated, and traced the progress of the 

 scatter during the succeeding 24 h. The site was outside the surf zone, 300 m 

 offshore and opposite the Scripps Institution of Oceanography at La Jolla, in 

 a water depth of 3 m. The average wave height was 38 cm and the average 

 period 14 sec. The direction of wave travel was approximately onshore. 



Putting the velocity of these long waves at \/{gh) = 540 cm/sec, relation (14) 

 predicts a shorew^ard wave drift, u, along the bed of 2.7 cm/sec (fixed bed), 

 and on the very rough evidence given by Bagnold (1947) the velocity, Ub, of 

 sediment drift over a sediment bed should be about one third of this, namely 

 1 cm /sec. 



The mean sediment size was 0.0125 cm, and the mean ripple height, -q, was 

 about li cm. If, as a reasonable estimate, we take b = 2, the average migration 

 velocity Ug should be 0.05 cm/sec, assuming that the motion is due wholly 

 to bed load. If an appreciable proportion of transport is in suspension the 

 migration velocity Ug would, of course, be larger. 



Seven and one-half hours after the exj^erimental re-deposition of the marked 

 sam])le the pattern of the scatter was such that the greatest migration distance 

 shoreward from the point of re-deposition was 30 m. This gives an average 

 speed of 0.1 cm/sec in the onshore direction. The rapid onshore migration was 

 in ])art due to transport of sand in suspension. During the stronger surges 

 accompanying the occasional largest waves, a vortex of suspended sand ex- 

 tending approximately 15 cm above the bottom was observed. In such cases 

 individual sand grains may be carried across several ripples before being 

 deposited. 



Irradiated grains were found by core sampling to be distributed to a depth 

 below the surface approximately equal to the ri])ple height, which is just what 

 would be expected from the above reasoning. 



