dZp OZp (2 
bans aye m is the beach slope), 
Se Ovane 
i.e., the change in z occurring along the beach is small relative to change 
across profile and the beach profile variation over a distance dx is small 
but remains an infinitesimal of higher order than over a distance dy. 
For the same reason, the velocity of beach variation along the ox-axis 
dx/dt is small as compared to the beach variation along oy; therefore 
IZp Cbs IZp dy 
OxeMGit Oven ae 
and could be neglected. To evaluate the other terms it is simpler to refer to 
Figure 3. It is seen that the integral is equal to the sum of: 
(a) The change of volume of sand, dv/dt, due to the translation, 
dyg/dt, is the sum of the change of volume due to the horizontal 
translation (Fig. 4) 
(B + Cc) — (2) 
and the change of volume due to the vertical displacement 
(ve - yp) (3) 
where Vi is the ordinate characterizing the location of the bluff. 
c 
Aas Yb 
dD 
B 
_—— 
_-— 
_—— 
~~ 
_-— 
6 ———= Cc 
AY Ye 
Figure 4, Changes of sand volume due to translation 
of one beach profile. 
14 
