By differentiation equation (31) 
dKp (x) a 2 cos ae a Tm cos (20,) 
EI | NIA sin Gs AL 
7 Cos (2a,) 
COS \ aa erm [ocacteecae ani (4S 201) (32) 
Inserting this value in the littoral drift equation (22) permits the mathemat- 
ical model to completed. 
In summary, the variation of volume of sand dV/dt given by equation (6) 
is equal to the sum of: 
(a) The loss of sand by wind Que 
(b) The loss of silt Qs = K,B dy,/at where K, is the percentage 
of silt in the bluff. 
(c) The loss of sand by density current during storn, Qf. and 
loss by rip current (or brought upon by nearby river). 
(d) The quantity of sand dredged or (at the opposite) deposited 
during beach nourishment. 
(e) The variation of littoral drift along the ox-axis is 9Q,/9x. 
In a refraction zone alone, 9Q,/dx is given by equation (18) where K,, 
is given by equation (17). op is given by equation (16) as a function of 
A>, and a, by equation (11), with respect to the ox-axis. Also, 9a,/9x 
is given by equation (21). 
In a diffraction zone 9Q,/3x is given by equation (22) instead of equa- 
tion (18) and the diffraction coefficient Kp by equation (31), and dKp/dx 
by equation (32) for a wave spectrum. ap is now given by equation (23) and 
dap / ax by equation (25). 
Since all the phenomenological equations have been established, it is more 
convenient to express them in dimensionless form. The ''general" equation ex- 
pressing the sand budget balance can still be written. (The loss terms have 
been dropped for simplicity and can easily be included if necessary.) 
Ys Gb) a ey Oe 
Golestehe We) aare ore Vb) mes a Do ae ae (33) 
For an analysis, this equation is considered in dimensionless form. Let 
e length 
B, + De 
where Bo is chosen later 
+ At 
—————— (35 
G34 Dae 
BS DD 
Q = 5 KAKs sin 2op (36) 
a2 
