Oceanic Island Wake Flows in the Laboratory - Modeling Atmospheric and Oceanic Flows - page 266

magnitude of the local vorticity exceeds unity and small-
scale three-dimensional unstable perturbations tend to
destroy completely the anticyclonic eddies. The horizon-
tal and vertical scales of the perturbation decrease when
the Reynolds number or the spatial resolution increases, in
agreement with the linear stability analysis of the unsta-
ble inertial or centrifugal modes [ Potylitsin and Peltier ,
1998; Kloosterziel et al. , 2007; Kloosterziel and Carnevale ,
2008; Plougonwen and Zeitlin , 2009]. The Princeton ocean
model (POM) was used by Hasegawa et al. [2009] to sim-
ulate a uniform surface flow past a small square oceanic
island ( D = 10km) with a high horizontal ( x = y =
1km) and vertical ( z = 10m) resolution. This study
focuses on the dynamic impact of the wake flow (eddies
and vertical mixing) on the biogeochemical cycles and
the phytoplankton bloom. For this intense submesoscale
wake, when Ro I =2, α

2000, the anti-
cyclonic boundary layer does not roll up to form coher-
ent anticyclones while cyclones are periodically shed and
remain coherent even with a strong relative core vorticity
( ζ/f =4

0.08 and Bu

5 according to Figure 2a by Hasegawa et al. ,
[2009]). In the anticyclonic shear only small turbulent
perturbations are visible on the vorticity field. Such small-
scale and three-dimensional instability did not appear in
previous numerical studies of oceanic wakes probably due
to the limited vertical resolution.
A large rotating tank, such as the 13 m diameter Cori-
olis plateform, was needed to study the three-dimensional
destabilization of rotating wakes confined in an upper
shallow-water layer ( α

−

Figure 14.7. Dye visualization of anticyclonic destabilization
within an upper shallow-water layer ( h c = 5 cm) corresponding
to Ro I

1). Small-scale disturbances
were first revealed by qualitative dye visualization in anti-
cyclonic eddies (Figure 14.7) when the island Rossby num-
ber exceed a critical value around Ro I

1.5, and Re = 10000 [ Teinturier et al. ,
2010]. Different dye colors were released on each side of the
cylinder ( D = 50 cm): black (red) in the anticyclonic (cyclonic)
boundary layer. For color detail, please see color plate section.

1, Bu 0.5 −

0.8 for a large

Reynolds number Re 5200 and a weakly stratified

layer N/f 5[ Teinturier et al. , 2010]. The typi-

cal horizontal scale of these unstable disturbances seems
to be fixed by the upper layer thickness rather than the
island radius. However, unlike experiments having large
or finite shallow-water ratio [ Tarbouriech and Renouard ,
1996; Stegner et al. , 2005], the PIV measurements within
the shallow-water layer ( α

4 −

Surprisingly, the core vorticity of both cyclonic and anti-
cyclonic eddies keeps high values for a long time:

| ζ 0 /f |

4 5. The cyclone-anticyclone asymmetry appears only

on the velocity profiles: The maximal azimuthal veloc-
ity of the anticyclone decays much faster than its
cyclonic counterpart. This anomalous decay of the mean
azimuthal velocity profile is the experimental signature
of the growth of inertial perturbations at the edge of
an intense anticyclone. Similar signatures were found in
numerical simulations [ Kloosterziel et al. , 2007] and previ-
ous laboratory experiments [ Teinturier et al. , 2010]. These
experimental results show that the combined effect of
a strong stratification and a moderate dissipation could
strongly stabilize the intense submesoscale anticyclones.
Hence, the threshold for three-dimensional destabiliza-
tion of anticyclonic regions cannot be given by a single
Rossby number, the critical Ro I will crucially depend on

−

0.2) show that the negative
core vorticity of unstable anticyclones remains coherent
for several rotation periods (i.e., several days). Hence, the
shallow-water configuration seems to reduce the impact
of inertial or centrifugal instabilities in the vortex street.
For a higher stratification, this stabilization is even more
pronounced. Indeed, several intense anticyclones, having
a relative core vorticity down to ζ 0 /f = 3, were found to

be stable in a shallow and strongly stratified ( N/f = 14)
wake where Ro I = 1.7 and Re = 15,000 [ Lazar et al. ,
2013b]. Anticyclones become unstable for higher Rossby
numbers (Ro I

−

2) but close to the marginal stability
limit the signature of the inertial-centrifugal instability
is not clearly visible on the vorticity field (Figure 14.8).

≥