Geoscience Reference
In-Depth Information
Table 11.2.
Estimations of characteristics numbers of large scale oceanic and atmospheric cyclonic flows.
ν
eddy
(
m
2
/
s
)
Geophysical Flows
N
(rad/s)
γ
=
H/(L/
2
)
L
(km)
Bu
Ro
d
Antarctic Polar Vortex
0.01-0.001
0.0023
6000
0.025-0.9
0.5
0.1-10
0.022-0.22
Cold Core Vortex rings — 0.014-0.025 40-70 0.05-0.5 0.1-0.35 0.01 0.03-0.05
Gulf Stream 0.007 0.008-0.012 100 0.28 0.45 0.01 0.05
Antarctic Circumpolar Current 0.002 0.1-0.08 35-50 0.64-1.3 0.1-0.2 0.01 0.02
Agulhas Current 0.003 0.02 93 0.19 0.02-0.2 0.01 0.005-0.02
Note:
For the ocean
ν
eddy
the vertical eddy viscosity is dominated by Ekman layers, i.e.
ν
=0.01m
2
/
s[
Cushman-Roisin
, 1994]. For
the case of circular currents, the radius or otherwise the half-width current, i.e.
L
/2 is taken for Ro and Bu number. The estimations
for cold-core vortex rings are from
Olson
[1991] with for the maximum velocity a mean value of 1 m
/
s. Antarctic Circumpolar
Current values are according to
Gille
[1994], who measured current widths of 35-50 km driven by surface winds, for which a
wavelength of 150 km was found. The Rossby number is calculated from
U
/(
fL
), taking
U
=20
40 cm/s, and for
d
mean values
are used. The values for the Agulhas current are estimated from
Webb
[1999] and
Beal et al.
[2006].
−
they propagate. Therefore most evident applications are
oceanic, e.g. coastal fronts. To our knowledge, the possi-
ble existence of the RK instability in geophysical flows has
not been considered yet. Below we further discuss some
geophysical flows and their position in the Bu-
d
diagram
presented in Figure 11.3.
To compare present results on frontal stability with
fronts in nature, estimations of the nondimensional
parameter values of some geophysical flows are presented
in Table 11.2. The eddy viscosity is related to the friction
in the Ekman boundary layer. Further it should be noted
that the comparison with oceanic examples concern
mainly outcropping flows (since they are visible whereas
internal interfaces are not so often observed), in contrast
to the present experimental results for internal interfaces.
Supposing that the friction at the free surface is not so
large to have an important effect on the instability, we
compare these flows with the results presented in the
diagram of Figure 11.3. The modeled parameter regime
set by Ro, Bu numbers and the dissipation number
d
shown in Figures 11.3a and 11.3b almost covers entirely
the parameter space of the real flows represented in Table
11.2. Further, the comparison in Figure 11.3 shows that
we may well expect the occurrence of the RK instability
in oceanic currents. Wavelengths are about 1 to a 1
/
3
of the current width, which corresponds to the size of
the lenses observed in the ocean near the Gulf Stream,
suggesting that the RK instability is a possible candidate
that deserves further attention.
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Acknowledgments.
The authors acknowledge
Jonathan Gula for providing the figures for linear stability
in Figure 11.5, the contract CIBLE of the French region
Rhone Alpes for financing this project, and the calculation
centers IDRIS and CINES for the simulation time on their
machines. Further, the authors acknowledge two anony-
mous referees for their corrections to the manuscript.
