Geoscience Reference
In-Depth Information
14
Oceanic Island Wake Flows in the Laboratory
Alexandre Stegner
14.1. INTRODUCTION
remains small (10-50km) compared to the atmospheric
Rossby radius (
1000km). Hence, several experimental
studies neglect the rotation and take into account only
the atmospheric stratification [
Etling
, 1989;
Rotunno and
Smolarkiewicz
, 1991] and the three-dimensional impact of
the orography which may trigger both a wave [
Johnson
et al.
, 2006] and a vortex wake. On the other hand, in
the midlatitude oceans the Rossby radius associated to
the first baroclinic mode [
Chelton et al.
, 1998] is much
smaller (10
∼
One of the first rewards of meteorological satellites
was the regular surveillance of cloud patterns over poorly
observed oceanic areas. Many fascinating new patterns
emerged, one of the most striking being the vortex
streets downwind of small isolated islands [
DeFelice et al.
,
2001]. At first glance, such atmospheric vortex shedding
looks similar to the incompressible two-dimensional von
Karman street which forms behind a cylindrical obstacle.
The classical two-dimensional wake is controlled by a sin-
gle parameter, the Reynolds number Re =
U
0
D/ν
where
U
0
is the free upstream velocity,
D
is the diameter of
the cylinder, and
ν
is the horizontal molecular viscos-
ity. If 1
<
Re
<
40, a laminar separation is obtained and
two steady vortices are formed immediately behind the
cylinder where they remain attached. For larger Reynolds
number a periodic vortex shedding of frequency
f
s
occurs.
The dimensionless shedding frequency, in other words
the Strouhal number
S
t
=
f
s
D/U
0
, increases with the
Reynolds number and approches an asymptotic value of
S
t
60km) and becomes comparable or smaller
than the typical island radius
R
. Hence, in the ocean the
rotation cannot be neglected and we could encounter both
mesoscale (
R
larger or equal to
R
d
) or submesoscale (
R
smaller than
R
d
) wakes. Surprisingly, the dynamical dis-
tinction between these two types of oceanic wakes was
done only recently. The aim of this review is to present the
most recent laboratory and theoretical results on the vari-
ous dynamical regimes which control an idealized oceanic
Karman wake at the mesoscale and submesoscale.
Considering oceanic flows, an important distinction
should be made between shallow- and deep-water wakes,
depending upon whether the dominant boundary stress
is associated with the near-shore bottom or the coastal
side of the island. If we consider shallow-water wakes,
generated by small islands in shallow shelf sea or estu-
aries, the bottom drag is the primary source of vorticity
generation [
Wolanski et al.
,1984,1996;
Alaee et al.
, 2004;
Neill and Elliott
, 2004]. For such configuration, where the
bottom friction and the vertical mixing are strong, the
stratification and the rotation are neglected. The equiva-
lent Reynolds number is then the island wake parameter
P
=
(U
0
D/κ
z
)(h/D)
2
,where
h
is the water depth and
κ
z
the turbulent diffusivity along the vertical. According
to experimental and numerical studies [
Wolanski et al.
,
1996], for small
P
the bottom friction prevents the forma-
tion of eddies; when
P
−
0.21 at high Reynolds number [
Wen and Lin
, 2001].
However, the direct application of these standard results
to geophysical wakes is often misleading because the dis-
sipation is highly turbulent and the molecular viscosity
must be replaced by a turbulent eddy viscosity which is in
general nonuniform and hard to estimate. Moreover, the
atmosphere and the ocean are affected by Earth's rotation
and the vertical stratification. We should then also take
into account the relative size of the island (or the eddies)
in comparison with the Rossby radius
R
d
, an intrinsic
horizontal scale that controls the dynamics of rotating
and stratified flows. For atmospheric vortex wakes, the
characteristic horizontal scale of the coherent structures
1 a stationnary dipole emerges in
the lee of the island and for larger values (
P
Laboratoire de Météorologie Dynamique, CNRS and École
Polytechnique, Palaiseau, France.
10 ) a peri-
odic shedding occurs. In this deep-water case, when the
