60 - 



square of the wavenumber. Such a module, however, is not part of the 

 software as presented in Appendix F. 



Theoretically, it is also possible to estimate the principal 

 wave direction without the absolute transducer signal similarly 

 assuming that there is only one wave direction per frequency. From 

 Equations A. 9, 4.10, and 4.11 the differential cross-correlations are 



S = k S cos^e = i k^ S (1 + cos 20) (A.AQ) 



S = k^ S sin^e = i k^ s (1 - COS 26) (^,50) 



y y 



S = k S sine cose = -^ k^ S (sin 20) (A. 51) 



X y 



for some frequency 6, so that an estimate of the wave direction might 

 be found from: 



2S 



n n 

 tan 2e = ^^ 



S - S (4.52) 



for some frequency 6. There exists four roots in the arctangent of 

 2 , as can be seen in Figure IV-4. It can be shown that two of these 

 roots are associated with maxima (and separated by 180°) and the 



