y(x,t) 



q 



d/ett 



/t 

 = /•*"[ 



to(t - r> + 



2 // r 2 

 -x /4e£ 



d5 



(49) 



The shoreline behavior is composed of one contribution that evolves roughly 

 proportional to the square root of elapsed time and another contribution which 

 is a periodic oscillation that damps out along the x-axis with a decay factor 



Jii)/2e (both in the negative and positive directions). Consequently, beyond a 

 certain distance from the discharge the periodic effect of Equation 49 can be 

 neglected, implying that the solution may be approximated by Equation 47 only. 

 Because of the periodic variation in the discharge, sand waves are generated 

 from the river mouth. These sand waves propagate with a speed /2eu along 

 the x-axis, and the time lag between the oscillation in sand discharge at the 

 river mouth and a specific location is tt/4 + x/a)/2e . In Figure 25 the 

 shoreline evolution at specific locations in the vicinity of a point source of 

 sand discharge with a periodic variation in strength is shown as a function of 

 0.5- 



L0CRTI0N (x/L) 

 o.o 



3 4 



TIME (et/L J ) 



Figure 25. Shoreline evolution in the vicinity of a river discharging 

 sand with a periodic variation in strength as a function of time 



(oiL /e = 2 , 



= , q /<) = q /<} = 0.5) 



40 



