35 



if the effect of the slope, i, can be neglected. This relationship is 

 shown in the upper curve of figure 19, and it is noted that the effect 

 of slope can be neglected within the order of experimental error. 



The second question to consider is the depression of the trough 

 AH2 at the start of wave break. The desired information can be ob- 

 tained conveniently if we consider the ratio AH2/AH1 as a function of 

 Uo^o- The upper curve in figure 20 approximates the relationship. 



Evaluation of the energy flowing into the bar environment can be 

 made on the basis of the quantities Hi, AHi, and AH2IAH1. Un- 

 fortunately, the theory of shallow water waves is not complete enough 

 for an appropriate analysis, there being available no general energy 

 formula covering the case of breaking waves. 



It is necessary to justify the absence of ag and ao/Xo in the general 

 and transportation formulas in equations 13 and 18. It was established 

 that ao/Hi=f{ao/\o)- By multiplying both sides of the equation by 

 'Ko/ag, it can be shown that there is a one to one correspondence 



between ag/'Ko and \q/Hi. Inasmuch as Xo=^^ ' it may be stated that 



do/Xo and Hi/gT^ are uniquely related and the latter may replace the 

 former. Because of these relations the quantities Hi and Hi/gT^ are 

 sufficient to characterize, in a functional manner, the magnitude and 

 the shape of waves entering the bar environment. 



The movement of sand from the shoreward limit of the bar environ- 

 ment to the shore is controlled by the energy content of waves at the 

 instant of reformation. For the evaluation of the energy the quan- 

 tities H2, A/i, and A/2/A/1 are fundamental. H2 is the depth of water 

 at the point where wave reformation begins, A/i is the crest elevation 

 above the undisturbed level and A/2 the depression of the trough 

 below that same level. The relationship between these quantities 

 and the wave steepness ratio ao/Xo is given in figures 18, 19, and 20. 

 These relationships should be studied further. 



D. Energy distribution in the bar environment. — The ease with 

 which the mathematical expressions for the form and position of bars 

 is established results from the simplicity of the experimental pro- 

 •cedure. The tests represent conditions under a singular system of 

 waves and in the absence of tidal flow. Each test began with a smooth 

 sloping surface and a bar was allowed to form and attain a relatively 

 fixed position in association with the breaker; then, the quantities 

 having a bearing on the form of the bar were measured. The resulting 

 data is of the most elementary nature and really contains little infor- 

 mation on the beach processes involved in the production of the bar. 

 During the tests, however, attempts were made to observe these 

 processes qualitatively. 



Sand movement along the bar appears to take place in the following 



