Assuming a solution for this equation is known, the shoreline y can be calcu- 
lated from the equation 
t 
y(t,» = y(o,x) + [ = (t,x) dt 
9) 
In practice, the equation for Q is not solved in the above form. Implicit in 
the above formulation is the assumption that the function g exists. However, 
as shown in Figure 11, g is not single-valued if the maximum range of the 
angle a, is greater than approximately 41°. This difficulty may be removed 
by considering the equation for Q and y as a system subject to the boundary 
conditions for Q. Note that 
cos? (2(@) = 5) 40 j[, | (2 j 
L 
dg (Q)/aQ da, ox 
Hence, the equation for Q becomes 
a0) al) 1 92Q 
STE Ra EINE MRD // AULT NOE WARE (45 
Oe cy is (2¥/ax) ax ) 
0.6 
z = 0.25+ 55H /Ly 
0.5 eis 
os z = 0.75 
g 
£ 
ae) 
is] 
8 z = 0.50 
0.2 
z = 0.25 
0.1 
ao 
10 20 30 40 50 
INCOMING WAVE ANGLE (°) 
Figure 11. Transport function Q(a,) = cos a sin za, 
for selected values of z. 
28 
