30 



As noted previously, Gerstner's theory does not provide for mass 

 transport of the water in the direction of wave travel, the paths of the 

 water particles being, in the case of deep water, cnclcs. According to 

 the Stokes-Lcvi-Civita theory the paths are open; but are basically 

 circles modified by the effect of mass transport. The magnitude of 

 the motion is the same in either case, except as modified by mass 

 transport. The results listed in tables 5 to 7 show that the curves are 

 not closed, but open, indicating that mass transport does exist. The 

 measured values of the orbit radii are generally in fair agreement with 

 theory, with a tendency for the experimental values to be smaller than 

 the theoretical being shown. 



The results of the measurements of mass transport are not conclusive 

 except insofar as they confirm the existence of mass transport. Quan- 

 titative verification of the theory could not be made with the equip- 

 ment now available. The importance of mass transport in natural 

 beach processes should not be underestimated. It is, for example, a 

 possible explanation of rip tides, since on any extended ocean coast 

 there may exist a localized seaward current; i. e. a rip tide, in com- 

 pensation for the shoreward current of mass transport. 



For the case of shallow-water waves (section 6) the comparison of 

 wave length and wave velocity indicates agreement within the limits 

 of experimental error with both of the theories considered, the closer 

 agreement being with the Stokes-Struik theory. 



The comparison of proportion of wave height above still water level 

 is inconclusive, verification of either theory within the limits of experi- 

 mental error being indicated. 



The wave profiles show noticeably better agreement with theory 

 than do the deep-water wave results. Within the limits of error 

 agreement with either theory is indicated. 



The comparison of orbit semi-axis values shows, as for the deep- 

 water waves, a tendency toward smaller measured values than are 

 indicated by theory. However, the existence of mass transport is 

 clearly shown. The magnitude of the mass transport effect could 

 not be quantitatively verified, 



8. CONCLUSIONS 



1, All of the characteristics of the oscillatory wave in deep or shallow 

 water required by the irrotational wave theories have been reproduced 

 in the wave tank, with the exception of the wave profile, 



2, It has been shown that mass transport does exist, as indicated 

 by the theories of Stokes, but the theoretical magnitudes have not 

 been quantitatively verified, 



3, Since mass transport has been shown to exist, it follows that the 

 Gerstner and Laplace-Airy wave theories, which do not admit its 

 existence, are not applicable to the waves studied. 



