Ill- 110 



CO 03 



if 



A(^.u) = I 1 - 4Ya^ I I v{l,m)Z{l-a,m-8)dldm^ b{X-a)&{u-B) 



(III-141) 



+ 4 Y^a^ Z(X - a,u - B). 



The term 4 y^ o^ Z(X-a,|a - 0) gives the intensity of the nonspecular waves, 

 while 



CD 00 



i) 



CI =i.4ya^ \ I v(l,m)Zil- a,m-d)dldm (III-142) 



spec 



-00 -co 



gives the intensity in the specular direction, where l^ + m^ + v^ - l . We will now 

 concentrate on an analysis of this latter term. 



Marsh,etal. describes the surface by using the Neumann-Pierson energy spectrum 



2 



\a) s / 



A^((ju) = — e '" " ' cm^sec (III- 143) 



where 



c = 4.8 (10*) cm^sec-^ 



g = acceleration due to gravity - 980 cm sec"^ 



s = wind speed in cm sec"'"' 



ou = angular frequency in rad. sec"'"' 



Using the assumed isotropy of the surface they find that Z(r), the normalized 

 autocorrelation function of the surface, is given by 



00 



Z (r-) = -^ I J. (— j A^(a))duj (III-144) 



2h^ J^ \ g / 



artbur KTi\n\t3nt. 



S-7001-0307 



