communication). The values of beach slopes for the various conditions 

 (Table 7) are illustrative of expectable trends in slope modification only 

 and are not recommended for the designing of future beach nourishment 

 projects at Virginia Beach, without qualifications. For a further insight 

 into the problem of slope modification the reader is referred to the entire 

 paper of Eagleson, et al. (1963), especially the section on the equilibrium 

 beach profile (1963, p. 43). 



A brief investigation of dynamics in the swash-backwash zone was also 

 made utilizing the expression of Ippen and Verma (1953) and the data of 

 Figure 2 and Table 5. 



Their equation, adapted here and solved for slope angle, is of the 

 form : 



-i -0.3 



V e = 0.12w S^ £- (S s - 1.01) (24) 



L k e 



where 



V e = the mean backwash edge velocity just large enough 

 to initiate movement of a given sized particle 



w = grain terminal fall velocity under natural conditions 

 (ft/sec) 



d n = grain nominal diameter (feet) 



S s = specific gravity of grains (2.65) 



S = slope of energy gradient 



k e = effective hydraulic roughness length (2.5 k, where k 

 is average grain diameter of bottom) 



To approximate Ve , the maximum backwash velocity and depth were 

 determined at the midpoint of the slope and the following relation solved 

 for V e : 



_ _ f log (1 + t d / a )l 



V max = V P ' _1 on 



where t d = depth of flow and a = the boundary — reference axis distance. 

 Surface samples of the sand were taken at the grid points or along the 

 single lines shown in Figure 2, immediately after recession of the backwash. 

 Backwash velocity was determined by introducing dye at slack uprush and 

 timing its movement over a measured distance downslope. (Ten-minute 

 averages of the heights of the plunging breakers at 13th Street and at Elm 

 Street showed 0.9 and 1.2 feet, respectively, for samples taken on Figure 2.) 



17 



