The determination of these three quantities is given from sand 
budget investigations. 
(b) A general term, M(x,t), expressing the local variation in 
the sand budget due to loss of sand by rip currents along groins, 
and to sudden dumping of sand in case of beach nourishment or flood. 
(c) The variation of littoral drift along the ox-axis which is 
re) 
OQa(S) > One 2 Cbg) So ae dx (7) 
Many formulas in literature sources express the rate of longshore transport, 
Q,, as a function of the incident wave energy along a straight shoreline. Long- 
shore transport is also a function of the sand characteristics (size distribu- 
tion and density), wave steepness, beach slope, etc. 
The form of this formulation on shoreline evolution is of paramount impor- 
tance. In particular, determination of the relative rate of sediment transpor- 
ted in suspension and by bedload is very important since this ratio influences 
the loss of sediment by rip currents. 
Such evaluation is beyond the state-of-the-art, and any improvement would 
require a major effort beyond the scope of the present investigation. Any im- 
provement in the longshore transport rate formula could eventually be introduced 
in the model at a later date. Therefore, it is assumed that the rate of sedi- 
ment transport is independent of density and size and depends solely on the 
longshore energy flux, P,, by the empirical relationship 
On) Shad, sO ID, (8) 
where Q, is in cubic yards per year. 
P,» is in foot-pounds per second per foot of shoreline and is expressed by 
the relationship (U.S. Army, Corps of Engineers, Coastal Engineering Research 
Center, 1977) 
2 
- OF BND ae 
Po 64 TASK) sin 2c, (9) 
where 
Kp = refraction coefficient from deep water to the line of breaking 
inception 
T = wave period 
H, = deepwater wave height 
a, = angle of the deepwater wave with the shoreline 
ap = angle of breaking with the shoreline 
Note that this equation expresses implicitly the rate of littoral drift 
along a straight shoreline in terms of breaking wave characteristics (except 
for the deepwater wave height, H,). The equation is assumed to hold in case 
16 
