an N TE TTE P EE ER DEE AA A 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
co co inc 
V. t) 7 35 kn je mn X (5.1) 
= =00[]==00 
t T Sim 
is -ik x of 
Vea) 7 ur | fee mt ax, (5.2) 
T 
7 TT 
where we have defined the generalized coordinate, x and wave vector k 
A ky m 
X = (6.1) k = = (6.2). , 
3 + mno. à 
t n 
m is the zonal wavenumber, and 
sin 21 
is the nth discrete angular frequency (Fig. 3). Y(k__) is the space-time 
spectrum of y, defined on integer wavenumbers m and”FRequencies GL 
corresponds to a double Fourier transform of y over the (synoptic rectangle 
D = [-m,m]X[-T/2,T/2] oriented parallel to the A,t axes (Fig. 4). 
$ (a) (b) 
r l^ k, 
ON Du. 
f urn = N ky 
7 A y b e A D, er 0s 
e. I / | 
d Do / | Note 
T i and 
NE =F x I : 
"E c + de 4 À 1 1 equi 
iy . AR stri 
s J^ ks Thus 
hs 
-1/2 
wher 
Fig. 3 Coordinate geometry in a) physical plane. Asynoptic 8, r coordinates are hybrids of longitude and time. 
Because of zonal periodicity, each element D. is equivalent to its periodic image; hence the integration 
may be performed over the strip of elements Qiong the 8 axis. b) Transform plane ky» kes k., k, are 
wavenumber components along respective axes. 8 
158