y,(t+dt) vg (t) Yq (t + dt) Yo (0) 1 
Figure 3. Change of beach profile. 
of translation is dD/dt, the perturbation can be defined only by a 
horizontal displacement. At the deepwater limit, D,, the horizontal 
displacement characterizing the rate of change of the average beach 
slope is defined by 
95, (x,t) 
ot 
so that 
The quantity of sand within the considered domain at time (t + dt) is 
vp 
V(t + dt) = ih apy (Epp pe \ cle). chy (GD) 
0 
and the variation 
Y, dz 
V 1 6 eas 
ae i = dy YY, and 0 are fixed limits) 
VI OZ OZ OZ 
Ge [es en 
dt 0 at Oy cle 9 Bee” eke 
where 9z,/0x is the variation of beach elevation along the ox-axis. Since 
the angle of the beach with the ox-axis is small 
13 
