The radian frequency is given by o. The relationships between the east- 

 west and north-south velocity components and the rotating Fourier component 

 representation are given by: 



U (t) = 1 ( [A(a) cos(at + *(a)) + C(a) cos(at + e(a))] da 



(2) 



U (t) = 1 f [A(a) sin(at + «t.(a)) - C(a) sin(at + e(a))] dc 



where A and 41 are the amplitude and phase of tne anticlockwise rotating 

 component, and C and e are the amplitude and phase of the clockwise 

 rotating component. In terms of the Fourier coefficients of the east- 

 west and north-south velocity components, the amplitudes and phases are 

 given by: 



A = 1/2 [(a + b )2 + (a - b )A 

 |_ 1 2 2 1 J 



C = 1/2 [(b^- aj)2 + (b^ + 82)2"] 



1/2 

 1/2 



tan 



4 



= 



a 



2 



- 



b 



1 



a~ 

 1 



T 



b 

 2 



tan 



e 



= 



b 



1 



+ 



a 

 2 



b~ 



2 



- 



a 



1 



(3) 

 (4) 



(5) 

 (6) 



Of particular interest for this analysis are the following rotary 

 spectra parameters: 



Clockwise energy spectrum: 



Ec = 1/2 ? (7) 



Anticlockwise energy spectrum: 



Ea = 1/2 A^ (8) 



