Geoscience Reference
In-Depth Information
m3sv7_grey barotropic/t-avg
Ψ
and E-vectors
8
6
4
2
0
-6
-4
-2
0
2
4
6
8
x
(cm)
E
-vector divergence(cm/s
2
)
-2.3e-03
-1.1e-03
1.5e-04
1.4e-03
2.6e-03
Figure 1.8.
E
vectors for chaotic flow in the annulus. The black contour lines show the assimilated barotropic time-averaged
horizontal stream function (contours below the middle of the range are dotted), and the grey vectors are the barotropic time-
averaged
E
vectors. The shading shows the
E
-vector divergence: black is up to
10
−4
cm/s
2
, grey is between
10
−4
−
5
×
−
5
×
cm/s
−2
and +5
10
−4
cm/s
2
, and white is above +5
10
−4
cm/s
2
. The flow is at
= 3.1 rad/s with
T
b
−
4.02
◦
C. (Adapted
×
×
T
a
≈
from
Young and Read
[2013] with permission of John Wiley & Sons, Inc.)
Based on sequences of laboratory measurements assim-
ilated into a Boussinesq Navier-Stokes numerical model
of the annulus,
Young and Read
[2013] found that local-
ized, small-scale eddies shed from the cyclonic troughs
of a large-scale baroclinic wave mode may be consistent
with a localized baroclinic instability. Figure 1.8 shows the
E
vectors [
Hoskins et al.
, 1983;
James
, 1994] for these mea-
surements at the highest rotation rate investigated. The
barotropic
E
vector is a horizontal vector defined from cor-
relations between the
x
cylinder, cyclonic cyclogenesis between the convergent
region and the outer cylinder, and vice versa toward the
inner cylinder. For the baroclinic annulus flows consid-
ered,
Young and Read
[2013] found the
E
vectors became
more strongly convergent/divergent as the rotation rate
increased. This acted to reinforce the main cyclone but
weaken the part extending into the anticyclonic region,
associated with the shedding of small-scale vortices, and
doing so more and more as the rotation rate increased.
The main baroclinic wave was found to be barotropically
stable according to
Bell
's [1989] criterion, but the insta-
bility was consistent with
Kim
's [1989] observation that
baroclinic Rossby waves may be baroclinically unstable
if the internal Rossby deformation radius
L
D
is much
smaller than a characteristic horizontal length scale
L
representative of the large-scale wave, in this case com-
parable with the annular gap width
b
−
y
components of the horizontal
velocity
(u
,
v)
by
E
=
(E
x
,
E
y
)
=
(v
2
u
2
,
u
v
)
,
−
−
(1.14)
where the overbar represents a timeaverage and primed
quantities are deviations from the time-mean flow. Its
divergence provides a measure of the interaction between
the time-mean flow and transient eddies such that
∇·
−
a
. In this flow
L
L
D
with increasing supercriticality (smaller values of
) as the rotation rate increased (as
L
D
∝
1
/
), consis-
tent with an interpretation of the chaotic vortex-shedding
phenomenon discussed above as a secondary baroclinic
instability of the large-scale wave.
E
>
0 implies a tendency for eddies to strengthen the
mean flow [
Hoskins et al.
, 1983]. For
E
vectors pointing
in the positive azimuthal direction, there is anticyclonic
cyclogenesis between the divergent region and the outer
