According to small-amplitude wave theory, the components of the water 
particle velocity in the x- and y-directions for a wave traveling at an 
angle, a, to the shoreline (Fig. 1) are, respectively, 
_H gT cosh [k(z + d)] 
WS a: —— meOSheaunmcon” cosa (1) 
_H gT cosh [k(z + d)] ‘ 
Yay e EEE cos@ sina (2) 
where 
H = wave height 
g = acceleration of gravity 
T = wave period 
L = wavelength 
d = water depth 
k = wave number 
8 = wave phase. 
The last two terms are defined as 
27 
Ge cli 
and 
6 = kx - ot 
where t is time, and w the wave angular frequency 
27 
wo =— 
Th 
The y-momentum (alongshore momentum) per unit volume is pv where p is 
the water mass densitye The flux of this momentum in the x-direction 
(onshore) per unit alongshore distance and unit water depth is pvue Inte- 
grating over the water column and averaging over time produce the mean along- 
shore momentum flux in the x-direction per unit alongshore distance 
n 
oy = _ | dz (3) 
where the overbar denotes the mean with respect to time and n the water 
surface elevation. Substituting equations (1) and (2) into (3) and dropping 
terms of higher than second order produce 
sina (4) 
S = CS cosa) C 
xy 
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