Geoscience Reference
In-Depth Information
Table 7.1.
Dimensional and nondimensional topographic
β
parameters in the experiments performed on a large-scale plat-
form by
Flór and Eames
[2002] (column FE) compared with
the corresponding values in two experiments using medium-
scale containers by
Masuda et al.
[1990] and
Carnevale et al.
[1991] (columns M and C, respectively). Considering that in
the ocean
f
(a)
Lifted
cylinder
Shallow
9m
10
−4
and
β
10
−11
m
−1
s
−1
, and a mesoscale
≈
≈
10
5
m, yields a nondimensional,
Slope
vortex with length scale
L
≈
Generated rossby wave
planetary parameter
β
≈
0.01.
Deep
Cyclonic vortex
M (1990)
C (1991)
FE (2002)
s
(slope)
0.333
0.133
0.053
(b)
f
(s
−1
)
4
1.2
0.25
H
(m)
0.24
0.171
0.35
Shallow
β
t
(m
−1
s
−1
)
5.55
0.933
0.038
L
(m)
0.05
0.05
0.1
β
t
=
Lβ
t
/f
0.069
0.039
0.015
as an alternating pattern of clockwise and anticlock-
wise circulation cells translating westward. Because of the
dynamical equivalence (7.20), similar oscillations are also
generated over a topographic slope, and they are usually
referred to as topographic (Rossby) waves. Because these
waves are associated with conservation of potential vor-
ticity, their frequency is subinertial [
Brink
, 1991]. When
generated near the coastline, the waves are also referred
to as continental shelf waves, and they travel along the
coast with shallow water to the right (left) in the North-
ern (Southern) Hemisphere. They can also travel along a
submerged slope [
Rhines
, 1969].
Since wavelike motions are in general very weak fea-
tures, fine observations are required to obtain quantitative
measurements. In addition, Rossby waves rapidly spread
and occupy wide areas, so a large facility is necessary to
detect them. This has been done in the Coriolis platform
in different studies. For instance,
Pierini et al.
[2002] con-
ducted experiments in a straight channel with a bottom
topography consisting of a linear slope separating two
regions with depths 0.3 and 0.6 m. The length of the chan-
nel was 4.3 m, and the width was 2 m, so the slope was
about 0.3/2 = 0.15. Wave motions were generated by using
a wavemaker consisting of a paddle oscillating in front of
the topographic feature. The rotation periods of the plat-
form in different experiments were between 35 and 50 s,
while the period of the wavemaker was 90 s. Under these
conditions, the authors measured the horizontal velocity
field on the free surface and detected three alternating
patches of opposite circulation along a distance of 4 m
over the topography (see their Figure 7.3). The duration
of the longest measurements is about 8 min. The authors
concluded that in all the analyzed cases the first Rossby
normal mode was generated.
Deep
(c)
Shallow
Deep
Figure 7.3.
Preliminary experimental study of topographic
waves excited by the passage of a cyclonic vortex (unpub-
lished results by Zavala Sansón and van Heijst). (a) Schematic
view (not to scale) of the experiments: A cyclonic vortex gen-
erated by the collapse technique drifts along the topographic
slope and generates topographic Rossby waves traveling with
shallow water to the right. (b) Relative vorticity surfaces mea-
sured in a horizontal plane at time
t
=14
T
, with
T
= 30 s the
rotation period of the Coriolis platform. The domain shown
is a 3.5 m
1.8 m rectangle. The submerged slope is 0.5 m
wide (approximated separation between dashed lines) and cen-
tered in the figure. The vortex is generated near the lower
right corner. The small, strong cyclonic vortex at the shal-
low side is a spurious vortex generated during the experiment
and does not play any role on the evolution of the topo-
graphic waves over the slope. (c) Corresponding surfaces of
the velocity component
v
, perpendicular to the topography
contours. For color detail, please see color plate section.
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