y(x,t) = A cos ax e 



2 

 -a et 



(44) 



for t > and -« < x < °° . 



Le Mehaute and Brebner (1961) and Bakker (1969) give this solution. A non- 

 dimensional diagram of the shoreline evolution of an initially cosine-shaped 

 beach is shown in Figure 23. 



0.5 1 1.5 



ALONGSHORE DISTANCE (x/L) 



Figure 23. Shoreline evolution of an initially cosine-shaped 

 beach (a distance of one beach cusp height added to the 

 shoreline position) 



Sand Discharge from a River Acting as a Point Source 



54. If a river mouth is small in comparison to the area into which it 



is discharging sand, the discharge may be approximated by a point source. The 



sand discharge from the river or the strength of the point source is denoted 



3 

 as q and is a function of time. (The units of q_ are m /sec.) A solu- 

 K K 



tion may be obtained by considering the continuous sand discharge from the 

 river to be the sum of discretely released quantities of sand at consecutive 



37 



