The deepwater limit of the beach is y = Ye: (This limit defines the con- 
tour line where the sand is no longer moved by wave action.) The water depth 
at y= y, is D,. It will be assumed that D, remains constant as sea level 
and beach profiles change. Therefore, dzg/dt = 3z,/odt. 
B is the height of the bluff in case of erosion, i.e., when dV¥o/at < 0, 
and) the jhetght of the berm incase) of accretion aes), when ioye/.ot On (Ealoeme)) 
EROSION ACCRETION 
Figure 2. Height of bluff or berm. 
The quantity of sand over a stretch of shoreline, Ax = unity and bounded by 
theydatums9z 5" 0) sy) —) 0, andiithelbeach) profile iz7 yy atetime sy stamps 
Y 
We] | ater) ae 
0 
Assume that, for some reason, the beach profile changes during an infini- 
tesimal amount of time, dt. A further assumption is that the initial beach 
profile which is considered at time, t = t;, could be the normal "equilibrium 
profile." (The equilibrium profile may never exist under varying prototype 
conditions (similarly two-dimensional waves never exist), but it is a conven- 
ient idealized concept which could be approached in two-dimensional wave tank 
experiments. In this case, it could be defined as the statistical long-term 
average beach profile which exists under a given wave climate. The model here 
is actually independent from this definition. ) 
The departure and modification from this initial beach profile can be 
characterized by (see Fig. 3): 
(a) A translation in the yz plane defined by an elementary 
vector of components. 
IV dD 
re ake 
where dD/dt is the rate of change of sea level. Note that this 
translation is independent from the beach profile and, in particular, 
if the beach profile normally exhibits a number of significant bar 
formations, under normal conditions the translation will reproduce 
this characteristic at the same water depth. 
(b) A perturbation characterizing the departure or variation 
from the initial profile. Since the rate of the vertical component 
12 
