Ming-Shun Chang 
AL = 2 Co(w;r = (nD, 0) ) aie i ee 
aug le 2. (wiz? = (nD, 0) ) (2. 8) 
By arranging the probes to measure wave elevations such that one 
can calculate the Co's and Q's upto # = (ND, 0) , the coefficients 
Ap, Aj, By, .-- Ay» By can be readily obtained from (278). “The 
relations in equation (2.8) are simple and they form the basis for 
the experiments described below. 
The accuracy of the approximation of equation (2.7) is de- 
pendent on both the order N and the non-dimensional parameter 
w°D/g . For given N and D the angular resolution, 6 , , is defined 
as 9, = sin ee 2 B . Physically this is a measure of the width of 
the angle over hee a narrow band wave-spectrum is spread. @, 
increases with decreasing w ; that is the angular resolution increases 
with increasing wave length. On the other hand if N and » are given, 
then 9, increases with decreasing probe separation, D. Fora spe- 
cific experimental setup, D can be adjusted for optimum results. 
As an example consider a narrow band directional wave spec- 
trum which satisfies 
k,+ Ak 
i 
2 
a 
e 
or 
+ 
— 
i 
2 
= 
e 
Fr 
“al 
I 
Va 
Nw 
< 
iT] 
So 
Otherwise 
where C(w) is an arbitrary function of frequency w and 2Ak, is 
the band width of the wave number k, . The directional spectrum can 
then be represented by a delta function, 6 , and its Fourier represen- 
tation is given by 
S(k,;@) = C(#) Dd (k D - kD) 
co 
C(#) Dj} 1 
en ree a re = 
= E ) | cos n(k) Kg)? | (2, 20) 
i ll 
where n= 1,2, ... THe nth order approximation gives 
1342 
