SECT. 3] BEACH AND NEABSHORE PROCESSES 523 



in the whole water body. It takes no account of general water drifts relative to 

 the bed boundary, such as may be caused by wind, tides and other agencies. 

 Water motions due sj)ecifically to the passage of waves must, therefore, be 

 superimjDOsed on any other motions that may exist. 



It is usual in the experimental study of wave effects as such to prevent any 

 drift of the water as a whole by confining the water within a closed channel. 

 Under these simplified conditions classical theory predicts, and experiment 

 confirms quantitatively, that in deep water a wave train of finite height causes 

 a drift of surface water in the direction of wave travel, and a corresponding 

 return drift beneath. 



When in shallow water the wave oscillations extend down to the bed boundary, 

 classical wave theory, which neglects all boundary drag, permits the return 

 drift to extend down to the bed. Experiment (Caligny, 1878; Bagnold, 1947) 

 has shown that on the contrary a forward drift occurs along the bed as well as 

 at the surface, the return flow being confined to intermediate depths. 



Longuet-Higgins (1953) has shown that classical theory can be extended to 

 take account of bed drag by the introduction of a thin boundary layer within 

 which the to-and-fro displacements close to the bed are assumed to dwindle to 

 zero at the actual bed surface. This extended theory predicts both the fact and 

 the magnitude of the forward bed drift, provided the boundary layer is supposed 

 free of mobile sediment. 



For a wave of full height H in a water depth h , the orbital velocity uq close 

 to the bed is assumed to be given by 



ttH I . , 27rh 



where T is the period and L the wavelength. If the depth to wavelength 

 ratio, h/L, is small, this reduces to 



H 



where C is the wave phase velocity. 



Taking wq as the orbital velocity just above the boundary layer, the predicted 

 drift velocity, u, is given by 



u 



5 llQ^ 



= M— C when h <t L. (14) 



It will be noticed that in the case of "long" waves {h<^L), a case where the 

 wave velocity C depends mainly on the depth h and not on the wavelength, 

 neither the orbital velocity uq nor the drift velocity u is, according to the 

 theory, dependent on the wavelength. 



Longuet-Higgins' theory, as applied to a sediment-free bed and as tested 



