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(a)
(b)
(c)
L
D
Figure 8.9
(a) Geostrophic flow along a boundary between stratified and mixed regimes,
with surface mixed layer depth D. (b) Growth of sinusoidal perturbation in the flow.
(c) Plan view of resultant baroclinic eddies, with length scale L.
The growth of a baroclinic instability is illustrated in
Fig. 8.9
. The process begins
with an initial sinusoidal perturbation of the front (a meander) which grows as
potential energy from the density field is converted into kinetic energy of a develop-
ing meander. The meander can eventually pinch off to form a cyclonic eddy. The
kinetic energy of the eddy becomes available through the interchange of water parcels
across the frontal boundary, a process which is most efficient when the exchange
is along paths having half the slope of the initial isopycnal surfaces (Pingree,
1978
).
According to perturbation theory of baroclinic flow (Eady,
1949
), the scale of the
most rapidly growing instability and hence of the resultant eddies will be given by:
q
g
0
D
4R
0
0
L
4
ð
8
:
8
Þ
f
where R
0
0
(m) is the internal Rossby radius which can be determined from the density
r (kg m
3
) between surface and bottom layers in the stratified water and the
thickness D(m) of the surface layer. For the example in
Fig. 8.8
, the observed values of
D
difference
D
20 km, which is of the same order as the observed scale of the eddy
motions (20-40 km). The corresponding time scale for eddy development is
r andD indicate L
2 days.
In principle, it should be possible to follow the evolution of developing eddy
systems from sequences of I-R images, but in practice this approach is frustrated
by the paucity of cloud-free images. It is also very difficult to follow the evolution of
an eddy from a research vessel given the scales involved and the continuous displace-
ment of the front by tidal advection. The mapping of temperature, salinity and
phytoplankton distributions in an eddy by Pingree and co-workers (Pingree et al.,
1979
) is one of the few such studies in the literature. Observation-based knowledge of
the detail of eddy processes is therefore limited and we are forced to rely on theory
and models to guide our understanding. Numerical models are able to simulate the
main features of the instability process in fronts (James,
1988
) while the laboratory
the complexity of eddy fields in fronts which may include contra-rotating pairs of
eddies. Some of the features in
Fig. 8.8
are suggestive of such eddy pairs rather than
individual cyclonic eddies (James,
1981
).
It is not yet clear why some fronts are subject to frequent eddy development while
others appear to be stable for much of the time. It may be that a sufficiently large
∼
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