524 BAGNOLD [CHAP. 21 



over a wide range of experimental conditions in the laboratory, has been found 

 (Russell and Osorio, 1958)i to be remarkably consistent with the facts except 

 in one significant case. There can be little doubt also that, in general, the 

 passage of a wave train creates a differential shear stress on the bed boundary 

 in the direction of its ])ro])agation. 



Unfortunately, Longuet-Higgins" theory, which involves the dynamical 

 distortion of the boundary layer as the waves pass over it, is inapplicable when 

 the boundary layer contains dispersed sediment. This is because the dynamical 

 properties of the layer substance will be changed in an undefinable way. 



Nevertheless, experiments in a wave tank (Bagnold, 1947) have demonstrated 

 qualitatively that the passage of "long"" waves over a sediment bed creates the 

 same forward drift of water close to the bed, together with a progressive trans- 

 jiort of sediment in the same direction. The drift velocity was found to be less, 

 but the drift extended to a greater height. 



It appeared, however, that contrary to the sediment-free case, both the drift 

 velocity and the sediment-transport rate for waves of a given height H decreased 

 to zero as the wavelength was reduced, although in all cases the waves would 

 be classed as "long". The larger the wavelength the greater the sediment- 

 transport rate was found to be, which seems consistent with experience in 

 nature. 



Thus in tentatively substituting u of relation (14) for Ue in (10) to give, 



*(wave drift transport) = K" ojUojC 



= K"<oHl2h, (15) 



it must be remembered that K" is likely to be a function of the wavelength. 

 This aspect deserves experimental study. 



The exceptional experimental condition mentioned above suggests that a 

 complication may be found when, as in the open sea, the constraints imposed 

 in a narrow channel are removed. When the channel width in Russell"s experi- 

 ments exceeded a certain multiple of the water depth, the wave drift along the 

 bed. which was otherwise uniform across the section, showed signs of in- 

 stability, becoming greater on one side than on the other. This suggests that, 

 in still wider channels, the wave drift may break up into circulations in a 

 plane parallel to the bed. If so, a random scattering of sediment would tend to 

 be superim]iosed upon a smaller forward drift. 



It is possible that the same kind of lateral instability gives rise to the well 

 known circulatory motion of the swash on a sand beach. 



Another complication is likely to be introduced in the open by the effects of 

 surface wind. Still confining attention to the sim])Ie conditions of a closed 

 channel in which it is possible to make controlled exi)eriments, a superimposed 

 wind in the wave direction would be expected to affect matters in two ways, i.e. 



(a) A direct wind drag on the water surface will, if sustained, create a 



1 This contains a useful summary by Longuet-Higgins of his theory, which he has 

 extended to include the case of a turbulent boundary layer. 



