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Similar experiments were carried out by
Cohen et al.
[2010]. In their study, the bottom topography extended
along an external annulus 4 m wide around the Coriolis
platform. The maximum fluid depth at the internal cir-
cumference was 1 m, while the depth at the external wall
was 0.6 m, so the slope is 0.4/4=0.1. The period of the plat-
form was about 30 s. At some point over the topography
the waves were generated by two short rods connected to a
motor. The characteristics of the rods determined the type
of excited wave. Field measurements were carried out over
an observation area at the opposite side of the wavemaker.
Using this information, the authors measured the velocity
fields and the corresponding velocity time series in order
to calculate the characteristic oscillations of the waves.
Their purpose was to analyze the dispersion relation of
the topographic waves measured in the experiments and to
compare the results with the dispersion relation of a har-
monic model (in which the cross-topography structures
of the waves are trigonometric functions) and a proposed
model based on Airy functions. Thus, this type of experi-
ments can be useful not only to observe the waves but also
to test analytical theories.
Topographic waves can be excited by the passage of a
vortex over a topographic slope. This has been the subject
of a series of recent experiments in the Coriolis plat-
form by the authors of this chapter. The bottom topog-
raphy consisted of a steep submarine escarpment that
has approximately a tanhshape with a maximum depth
of 0.8 m, a minimum depth of 0.55 m, and a width of
0.5 m, so the slope is 0.25/0.50=0.5. A cyclonic vortex was
generated at the deep side of the escarpment. This vortex
was generated by lifting a solid cylinder out of the fluid,
which creates a low-pressure zone and a corresponding
cyclonic motion. This method is referred to as the “col-
lapse technique”by
KloosterzielandvanHeijst
[1992]. The
presence of the bottom slope makes the vortex move along
the topography, as sketched in Figure 7.3a. These exper-
iments were performed over a 9 m long, straight topog-
raphy that covers a great part of the platform diameter.
Measurements of vorticity and horizontal velocity have
revealed the structure of the topographic waves. Figures
7.3b and 7.3c show the vorticity field and the velocity
component
v
transversal to the topography. The slope
is centerd along the
x
axis, so the upper part of the
figure corresponds to the shallow and the lower part to
the deeper part of the flow region. The graphs, covering
a domain of almost 4 m in the horizontal, are a com-
posite picture obtained from two cameras mounted in the
corotating superstructure of the platform. At the time the
photographs were taken, the vortex had already passed
theviewield,andinitswaketheRossbywaveisclearly
observed in the
v
field (Figure 7.3c), rather than in the
vorticity field
ω
(Figure 7.3b). The whole pattern drifts to
the left, along the topography, which is the topographic
compass direction “west.”This study was designed to per-
form quantitative measurements of the vertical velocity
component
w
in order to estimate the relevance of the
topographic waves on the vertical transport. The results
will be published elsewhere. Regarding vertical motions,
we shall now discuss a similar study on vortices over
submarine mountains.
7.3.3. Vertical Motions
As discussed above, a first approach in the modeling
of geophysical flows consists of considering the fluid
motion as organized in the form of vertical columns.
However, stretching and squeezing effects triggered by a
flow impinging on variable topography may drive verti-
cal motions and material transport. Some authors have
proposed these effects as a mechanism to explain the
upwelling of deep waters over seamounts or continental
slopes, which are nutrient-rich waters that in turn favor
plankton and fish abundances over these topographic fea-
tures [see, e.g.,
BeckmannandMohn
, 2002]. An equivalent
debate exists about the action of planetary Rossby waves
on the pumping of nutrients to the ocean surface [
Uzetal.
,
2001].
Laboratory experiments in large-scale facilities may
provide new insights not only in the horizontal but also
in the vertical flow fields generated by a vortex over a sub-
marine obstacle. This was recently done by
Zavala Sansón
et al.
[2012], who performed a series of experiments on
the Coriolis platform on the evolution of cyclonic vor-
tices over an axisymmetric mountain. The mountain con-
sisted of a solid, axisymmetric structure, with a maximum
height of 0.3 m above the bottom of the rotating plat-
form and a radius of 0.5 m. The large dimensions of
the experimental tank allowed to place the mountain far
enough (i.e., several mountain diameters) from the lat-
eral walls. The experiments reproduced the main results in
the horizontal velocity field observed in previous studies:
cyclonic vortices drift in an anticyclonic direction around
a conical hill due to the topographic
β
-effect associated
with the slope of the topography (reported by
Carnevale
et al.
[1991] using a medium-scale rotating tank). Another
important result is the generation of anticyclonic vortices
over the summit of a seamount, as shown in the numerical
simulations of
Verron and Le Provost
[1985].
How is the structure of the vertical velocity field when
a cyclonic vortex rotates around the tip of the moun-
tain? The measurements revealed that the flow in a vertical
plane across the mountain has an oscillatory charac-
ter associated with the orbital motion of the vortex
around the topography. This behavior was measured in
a number of experiments and was simulated numeri-
cally afterward. The simulations were based on the quasi-
two-dimensional model (7.17) that allows to solve the
