Geoscience Reference
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PC of EOF 1 explaining 42.6179% of variance
PC of EOF 2 explaining 9.7012% of variance
0.2
Re(PC)
Im(PC)
Re(PC)
Im(PC)
0.1
0.15
0.1
0.05
0.05
0
0
-0.05
-0.1
-0.05
-0.15
-0.1
-0.2
100
200
300
Time (s)
400
500
600
100
200
300
400
500
600
Time (s)
Real EOF1 42.6179%
Real EOF2 9.7012%
250
250
200
200
150
150
100
100
50
50
0 0
0
50
100
150
200
250
0
50
100
150
200
250
Figure 17.4. CEOF analysis of PIV measurements (given in corotating frame). Top: The principal component (PC) of CEOF1 (real
part black, imaginary part red) (left) and of CEOF2 (right). Bottom: Real part of CEOF1 (left) and of CEOF2 (right). The imaginary
parts of the two CEOFs are phase-shifted versions of the real parts.
vacillating wave regime discussed above. Classical Eady
modes are nondispersive, and we might conclude that
the first four EOFs do not resolve the nonlinear features
of the wave modes in the irregular flow. Hence, EOFs
from the noisy part of the spectrum need to be considered
to address the irregularity of large Taylor/small Rossby
number regimes.
Finally, in Figure 17.6 and Table 17.1 we show the vari-
ance distribution (in percent of the total variance) for the
first 12 wave modes m =1,2, ... ,12 along a transection
through the regime diagram, from the azimuthal flow
regime ( m = 0) to the slightly irregular m = 4 wave regime
(6.79
10 2
10 6
10 8 , 5.73
4.0,
T = 8K). The transition from m =0to m = 2 occurs
at ( Ta, Ro ) = ( 9.49
×
Ta
4.77
×
×
Ro
10 6 ,2.82 ) . A dominant wave with
m = 2 establishes, but other waves ( m =3, ... ,6)arealso
present in the variance spectrum. This indicates that the
flow with zonal wave number 2 exhibits some vacillations.
At ( Ta, Ro ) = ( 2.3
×
10 7 ,1.19 ) , the flow regime changes
to m = 3 and we can find this wave and its harmonics
×
 
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