One way to solve the problem would be to fit the directional spectrum 

 by sui analytic function of a and p and carry out the transformation and in- 

 tegration formally so as to obtain the spectrum as a function of frequency. 

 It was decided that this was too difficult so it was assumed that the direction- j 

 al spectrum was a constant over a unit square in the U(r, s) plane. Figure 

 11.19 illustrates schematically the assumed shape of the directional spectrum. 



The wave pole spectrum was determined in Part 10, and the AE values 

 for frequencies between 2Tr(K -— )/96 and 2it{K +-2)/96 were found. A fre- 

 quency of 2ii;(K --i)/96 corresponds to a period of 96/(K -4) and this in 

 terms of wavelength corresponds to a wave 5.12(96/K - -i) feet long. Con- 

 sequently the circle with a radius R* given by equation (11,11) defines one 

 boundary of that area in the U(r, s) plane which corresponds to a frequency 

 bound of the wave pole spectrum. 



(11.11) 



R*^ 



1 2 

 2i^(K -^) 



(96)2(5.12) 



The other boundary for a particular K is given by (11.12) 



(11.12) 



R* = 



1 ^ 

 2Tr(K + ^) 



(96)2(5.12) 



In the above, coordinates of the directional spectrum, have been 



192 



