Geoscience Reference
In-Depth Information
Boyer et al.
, 1984;
Stegner et al.
, 2005]. Dye visualizations,
such as Figure 14.6, reveal small-scale disturbances within
anticyclonic eddies when the Reynolds Re or the inverse
Ekman number 1
/E
k
was sufficiently large and the island
Rossby number reached or exceed critical values close to
unity: Ro
I
St
0.7
Re=200
Re=400
Re=800
0.6
Re=1000
0.8 [
Boyer and Kmetz
, 1983;
Boyer
et al.
, 1984;
Tarbouriech and Renouard
, 1996;
Stegner
et al.
, 2005]. When quantitative velocity measurements
were available, they showed a rapid decay of the negative
core vorticity to the limit
ζ/f
0.6
−
Re=200-300
0.5
−
1 while the cyclones
could keep higher values for longer times [
Tarbouriech
and Renouard
, 1996;
Stegner et al.
, 2005]. The symme-
try between the cyclonic and the anticyclonic vortices in
the lee of the obstacle is broken and only cyclonic eddies
could survive with large core vorticity. Besides, the latest
results [
Stegner et al.
, 2005] show that the strong elliptic-
ity of detached vortices behind the cylinder governs the
transient three-dimensional instability in the near wake.
However, the application of these laboratory results to
oceanic wakes could be misleading because these exper-
iments were performed with a tall column cylinder,
α
=
3
0.4
0.3
0.2
0.001
0.01
0.1
1
λ
Figure 14.5.
Strouhal number as a function of the relative inter-
face deviations
λ
=Ro
I
/
Bu for different Reynolds numbers.
The dashed zone indicates the range of the Strouhal number for
two and three-dimensional wakes at these Reynolds numbers.
The solid line corresponds to numerical simulations of cylinder
wakes in a rotating shallow-water layer.
10, and without any stratification while island wakes in
the deep ocean are conined within a shallow and stratified
surface layer. Therefore, recent numerical and laboratory
studies were performed with realistic stratification and a
small shallow-water ratio,
α
−
1.
High-resolution numerical models were needed to
capture the three-dimensional unstable motions which
emerged in the wake of an idealized island in deep water.
The regional oceanic model system (ROMS) was used by
Dong et al.
[2007] to solve the rotating primitive equations
with a high horizontal (
x
=
y
= 250m) and verti-
cal (
z
= 25m) resolution. For large enough Reynolds
number, when Ro
I
= 0.2-1,
α
14.5.1. Three-Dimensional Destabilization
of Two-Dimensional Wake
The destabilization of intense anticyclones in a rotat-
ing vortex street was first studied in an homogeneous fluid
layer [
Boyer and Davies
, 1982;
Boyer and Kmetz
, 1983;
0.01, and Bu
1, the
(a)
(b)
Figure 14.6.
Dye visualization of anticyclonic destabilization within a vortex street at (a)
t
=0and(b)
t
=0.8
T
0
when Ro
I
= 2.5,
Re = 150, and
α
=10[
Stegner et al.
, 2005]. The fluorescent dye was uniformly painted all around the cylinder (
D
=2cm)and
released in the boundary layer during the translation. The turntable rotates clockwise and the cylinder starts to move at
t
−
3
T
0
.
The experimental configuration corresponds to figure 2 (b).