27 



Obviously, the non-uniform transportation of sand is effected by the 

 total displacement of the water sm-face at a given point during the 

 passage of waves. If AiJi is the maximum elevation of the surface 

 above the undisturbed water level during the passage of the waves 

 and AHi the maximum depression, the total displacement is given 

 by LH. = tJIx^r ^^i- The relation between the rate of initial sand 

 transportation and the fall of the water surface is shown in figure 15. 

 It is apparent that correlation exists between the rate of sand trans- 

 portation and the total displacement of the water surface during the 

 wave passage. A clear picture of the correlation of surface displace- 

 ment with the rate of sand transport is obtained by considering the 

 dependence of the rate of sand transportation Q, upon AH expressed 

 in terms of dimensionless quantities. Three distinct regions must 

 be kept in mind in dealing with the problem of sand transportation 

 under wave action. The most important region has been referred 

 to previously as the bar environment, which is bounded seaward by 

 the point of impending wave break and shoreward by the point of 

 reformation of waves beyond the breaker; the limits of this region are 

 readily obtained in laboratory experiments. The remaining two 

 regions are: the one extending indefinitely seaward from the point of 

 impending wave break; the other extending to the shore line from the 

 point of reformation of waves. The laws of transportation of sand in 

 these regions are expected to be different. 



In this investigation only the movement of material in the region 

 of bar environment under initial conditions will be considered. The 

 assumption is made that the rate of sand transportation Q depends on 

 the total surface displacement t^H, the depth of water Hi at the point of 

 impending wave break; the period of the wave T; the characteristic 

 sand grain size doM-, the kinematic viscosity v] the densities of water 

 and sand p^, and p^, respectively; the gravity constant g; the slope ^; 

 and the sand dispersion coeflEiciento-p. The ordinary arguments of 

 dimensional analysis result in the general relationship 



-^2 = f (^H/Hi, pjp., J&OM^ JJJgr^2^ ^^^/27i, i, Cr,) (13) 



defining the law of sand transportation. In the equation the dimen- 

 sions of the initial deep water waves are missing, since the wave 

 characteristics are determined by T and AH. The last six quantities 

 may be considered constants for a given test hence it suffices to ^^Tito 



-^,=fiAH/H,) (14) 



