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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).
 
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