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a shallow fluid layer, both numerically and experimen-
tally. By quantifying the magnitude of the vertical motion
and the (nonzero) horizontal divergence with respect to
the primary swirling motion in the vortex cores, they
found that the three dimensionality of the shallow ( δ
Acknowledgments. The authors gratefully acknowl-
edge their colleagues and former Ph.D. students for
numerous fruitful discussions throughout the years:
Leon Kamp, Herman Clercx, Ruben Trieling, Rinie
Akkermans, Matias Duran-Matute, Andrzej Cieslik, Ron
Theunissen, Saskia Maassen, and Miguel Tenreiro. The
experimental work of the authors performed in the Cori-
olis platform in 2009 was funded by the 6th Framework
Programme of the European Commission within the Inte-
grated Infrastructure Initiative Hydralab III. The authors
gratefully acknowledge the scientific and technical help
of H. Didelle, S. Viboud, J. Sommeria, and L. Gostiaux
during our stay in Grenoble.
1)
dipolar vortex flow depends on the quantity Re δ 2 .Three
different regimes could be distinguished: (i) a quasi-2D
regime for Re δ 2
6, in which the flow is dominated by
viscous effects. In this case the secondary flow is negligi-
bly small; (ii) a transitional regime for 6
Re δ 2
15, in
which secondary motion inside the dipole can be observed
as well as a spanwise circulation cell in front of the
translating dipole. These 3D effects are rather weak, how-
ever, and they do not seriously affect the primary dipole
flow; (iii) a 3D regime for Re δ 2
15, in which the prin-
cipal dipole flow is seriously affected by the secondary
motions.
The flow behavior was examined for different initial
conditions, but these resulted in rather marginal differ-
ences in the Re δ 2 values of the transitional regime. The
agreement found between the experiments and the numer-
ical simulations underline the conclusion that the quantity
Re δ 2 is the crucial parameter characterizing the decay-
ing dipole flow. As this quantity is apparently the relevant
parameter in describing the two basic, generic flow struc-
tures (monopolar and dipolar flows), it is anticipated that
it is also the crucial parameter characterizing the three
dimensionalization of other types of shallow flows.
REFERENCES
Akkermans, R. A. D., A. R., Cieslik, L. P. J., Kamp,
R. R., Trieling, H. J. H. Clercx, and G. J. F. van Heijst (2008a),
The three-dimensional structure of an electromagnetically
generated dipolar vortex in a shallow fluid layer, Phys. Fluids ,
20 , 116,601.
Akkermans, R. A. D., L. P. J., Kamp, H. J. H. Clercx, and
G. J. F. van Heijst (2008b), Intrinsic three-dimensionality in
electromagnetically driven shallow flows, Europhys. Lett. , 83 ,
24,001.
Akkermans, R. A. D., L. P. J., Kamp, H. J. H. Clercx, and
G. J. F. van Heijst (2010), Three-dimensional flow in electro-
magnetically driven shallow two-layer fluids, Phys. Rev. E , 82 ,
026,314.
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tion at Great Meteor Seamount Part II: Retention potential of
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Mech. , 32 , 165-202.
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turbulence above topography, J. Fluid Mech. , 78 , 129-154.
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7.6. CONCLUDING REMARKS
We have described laboratory experiments on flows over
bottom topography in arrangements of different scales,
ranging from rotating fluid containers of more than 10 m
in diameter to fluid layers of a few millimeters in thick-
ness. The choice of the spatial dimensions depends on the
particular aspects of the flow that one is interested in and
also on the measurement resolution that one wishes to
achieve. As has been discussed, the dimensions of differ-
ent experimental facilities may imply different advantages
and disadvantages. For example, nonrotating shallow-
layer experiments with electromagnetic forcing in a thin
layer of electrolyte are characterized by a relatively high
damping rate, which puts a serious limitation on the use-
fulness of such a setup. In addition, recent experiments
have revealed that the fluid shallowness does not guaran-
tee the two dimensionality of the flow, and a more careful
scaling argument is required. On the other hand, large-
scale rotating experiments are often less easy to run (and
far more expensive) than the medium-scale O (1 m) exper-
iments, just because of their size. In any case, medium-
and large-scale facilities are ideal to study the effects of
variable topography.
 
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