Geoscience Reference
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(a)
Eigenvalues of covariance matrix (in % ot total variance)
30
20
First 10 eigenvalues
10
1
2
3
4
5
6
7
8
9
10
(b)
PC of EOF 1 explaining 37.0297% of variance
5
Re(PC)
Im(PC)
0
−5
−10
20
40
60
80
100
120
140
160
180
200
Number of rotations
(c)
PC of EOF 2 explaining 16.5096% of variance
5
Re(PC)
Im(PC)
0
−5
20
40
60
80
100
120
140
160
180
200
Number of rotations
Figure 17.10. (a) Variance spectrum of a CEOF analysis. (b) Real and imaginary parts of PC1. (c) Real and imaginary parts of PC2.
PC1 mainly captures the propagating wave whereas PC2 comprises a significant part of the low-frequency temperature forcing.
(a,c) and imaginary parts (b,d) of the CEOF show the
propagating anomaly at two different phases with a phase
shift of π/ 2. The patterns have to be read in the follow-
ing way: Figure 17.11a,c represent the flow at the begin-
ning of a cycle, and Figures 17.11b,d represent a quarter
of a cycle later. The fields displayed in Figures 17.11a,c
but multiplied by
CEOF2 (Figures 17.11a,b) clearly reveals that the wave
structure is prominent in the upstream and weak in the
downstream region. The pattern of the local CEOF1
(Figures 17.11c,d) is rather easy to interpret. It is clearly
dominated by a regular train of vortices slowly traveling
prograde towards the barrier. Note that the local CEOFs
have been computed independently from the full annulus
just for the local domain. Still, Figures 17.11c,d resemble
very closely the upstream part of the full annulus CEOFs
(Figures 17.11a,b). From the local CEOFs we find that
temperature anomalies are not circular but show a promi-
nent bulge that is opposed to the direction of the mean
flow. We also find that the temperature maxima and min-
ima do not correspond with the centers of the vortices.
With respect to these centers, the temperature anomalies
are shifted toward the inner cylinder and slightly down-
stream. We see that due to the bulges, a significant pos-
itive heat flux can be observed (positive anomalies are
transported inward, negative anomalies outwards). This
flux reduces the radial temperature gradient.
From Figures 17.11c,d we see further that the strength
of a vortex continuously increases until the anomaly
reaches the barrier. We further note a small cyclone within
the constriction of the annulus (Figure 17.11d). This
1 show the flow at half of the cycle;
Figure 17.11b,d multiplied by
1 give the flow at three
quarters of the cycle. A quarters of the cycle later the cycle
is complete and the starting point is reached again (that is,
Figures 17.11a,c).
CEOF1 computed for the full annulus (not shown) con-
tains a mix of waves and the forcing signal and is more
difficult to interpret than CEOF2. In the temperature field
we find the modulation pattern as an increase/decrease of
the temperature along the outer boundary. We also find
propagating wave structures and vortices in the upstream
region and a locally fixed but pulsating vortex in the
downstream region. This vortex can be seen even clearer
in a local EOF analysis of the downstream region and is
likely directly connected to the barrier and is not gener-
ated by baroclinic instability. The strength of the vortex
changes due to the oscillating meridional temperature
contrast.
 
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