A 9-month deployment of high-frequency radio (HFR) current meters and moored ADCPs in the lee of Oahu, Hawaii, gives some dynamical insights in the generation and evolution of vortices in the lee of islands. For mountainous islands lying in relatively strong and steady winds, such as the Hawaiian archipelago in the trade winds, vortices can be generated by Ekman pumping associated with orographic wind stress curls. An anticyclone generated in the lee of Oahu in October 2002 reaches a negative absolute vorticity for 4 days, before quickly decaying and broadening, possibly as a result of inertial instability. A large cyclone, generated in December 2002 in the lee of Hawaii, drifted northwestward and stalled southwest of Oahu in March-April 2003. Vortex Rossby waves developing on its periphery were observed by the HFRs with a northeastward phase propagation, 110 km wavelength and 16 days period

CHAVANNE, Cédric

FLAMENT, Pierre

GURGEL, Klaus-Werner

I-Revues

18èmeCongrès Français de Mécanique Grenoble, 27-31 août 2007
Observations of vortices and vortex Rossby waves in the lee of an island
Cédric Chavanne(1) & Pierre Flament (1) & Klaus-Werner Gurgel (2)
(1) School of Ocean and Earth Science and Technology, University of Hawaii
Department of Oceanography, 1000, Pope Rd, Honolulu, HI 96822, USA
(2) Institute of Oceanography, University of Hamburg
Bundesstrasse 53, D-20146 Hamburg, Germany
cedric@soest.hawaii.edu
Abstract :
A 9-month deployment of high-frequency radio (HFR) currentmeters and moored ADCPs in the lee of Oahu,
Hawaii, gives some dynamical insights in the generation andevolution of vortices in the lee of islands. For
mountainous islands lying in relatively strong and steady winds, such as the Hawaiian archipelago in the trade
winds, vortices can be generated by Ekman pumping associated wi h orographic wind stress curls. An anticyclone
generated in the lee of Oahu in October 2002 reaches a negative bsolute vorticity for 4 days, before quickly
decaying and broadening, possibly as a result of inertial instability. A large cyclone, generated in December 2002
in the lee of Hawaii, drifted northwestward and stalled southwest of Oahu in March-April 2003. Vortex Rossby
waves developing on its periphery were observed by the HFRs with a northeastward phase propagation, 110 km
wavelength and 16 days period.
Résumé :
Un déploiement de 9 mois de courantomètres radio haute-fréquence (HFR) et d’ADCPs mouillés dans le sillage
d’Oahu, Hawaii, donne un aperçu sur la dynamique des tourbillons dans le sillage d’îles. Pour des îles mon-
tagneuses soumises à des vents relativement forts et constants, comme l’archipèle hawaiien sous les Alizés, les
tourbillons peuvent être générés par pompage d’Ekman associé aux rotationnels du vent orographiques. Un an-
ticyclone généré dans le sillage d’Oahu en octobre 2002 atteint une vorticité absolue négative pendant 4 jours,
avant de rapidement s’affaiblir et s’élargir, probablement dû à une instabilité inertielle. Un gros cyclone, généré
dans le sillage d’Hawaii en décembre 2002, dériva vers le nord-ouest pour s’installer au sud-ouest d’Oahu durant
mars-avril 2003. Des ondes de Rossby de tourbillon se développant à sa périphérie sont observées par les HFRs
avec une phase se propageant vers le nord-est, une longueur d’onde de 110 km et une période de 16 jours.
Key-words :
vortices ; vortex Rossby waves ; island wake
1 Introduction
The Hawaiian archipelago, isolated in the middle of the Pacific within the North Equatorial
Current and trade winds, is an ideal natural geophysical laboratory to study obstacle wakes in
rotating stratified flows. We describe here ocean current observations by two high-frequency
radio (HFR) surface current meters and moored ADCPs, deployedfrom September 2002 to
May 2003 along the west coast of Oahu (Fig. 1). The currents were low-pass filtered with a
cutoff period of 3 days, to filter out tidal and inertial currents (Tf = 2π/f ∼ 33 hours), and
subsampled daily. The horizontal resolution is 5 km. The 9-month average circulation consists
in a northwestward current, increasing from less than 5 cm/snear the coast to 30 cm/s 60 km
offshore, corresponding to a vorticity of∼ 0.1f . The dominant winds are northeasterly trade
winds, and are affected by the island mountain ranges, yielding a wind stress curl dipole west
of Oahu. We focus on the periods between September to November 2002 in Part 1, when the
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18èmeCongrès Français de Mécanique Grenoble, 27-31 août 2007
variability was dominated by submesoscale vortices, and between March and April 2003 in Part
2, when the variability was dominated by vortex Rossby waves.
C1
A2
C2
Oahu
30 cm/s
current
−159 −158.6 −158.2 −157.8
20.8
21
21.2
21.4
21.6
21.8
ζ/f
−1 −0.5 0 0.5 1
HNL
0.1 N.m−2
wind stress
−159 −158.6 −158.2 −157.8
20.8
21
21.2
21.4
21.6
21.8
curl τ [N.m−3]
−1 −0.5 0 0.5 1
x 10
−6
Figure 1: Experimental setup: (left panel) mean surface currents fromHFRs and ADCPs (vectors) and
vorticity normalized by f (color), (right panel) climatological wind stress from QuikSCAT and airports
(vectors) and curl (color), and vortex center tracks during Fall 2002 (thick black line and pluses: cyclone,
thin black lines and x-marks: anticyclones, symbols one day apart). Locations of HFRs (circles), moored
ADCPs (triangles), and airports (diamonds) are indicated. Topographiccontours in gray (every 500 m)
and black contour for 0 m.
2 Vortices
2.1 Description
We define a vortex core as a region around a velocity minimum (the vortex center) where vor-
ticity dominates over stretching and shearing deformations:
ζ2 = (∂xv − ∂yu)
2 > (∂xu − ∂yv)
2 + (∂xv + ∂yu)
2 (1)
We define the vortex radius as the maximum distance between the center and the core limits.
Vortices with radii ranging from 5 to 50 km, smaller than the first baroclinic deformation ra-
dius (∼60 km, Cheltonet al. (1998)), dominated the low-frequency currents variability from
September to November 2002 (Fig. 2). 4 anticyclones were spun-u near the coast (see Fig.
1, right panel) during periods of strong trade winds, in the ar a of negative wind stress curl,
while only one small cyclone was spun-up during a period of weak and variable winds. One
anticyclone was particularly strong, its Rossby number reaching 1.1, and remaining above 1 for
4 days. Its vorticity then quickly decayed and its radius increased, before it drifted out of the
domain to the southwest.
2.2 Dynamics
Many mechanisms can lead to the formation of vortices in the lee of islands: lateral viscous
stress at vertical boundaries, bottom stress, vortex stretching and tilting, and Ekman pumping.
2
18èmeCongrès Français de Mécanique Grenoble, 27-31 août 2007
−5
0
5
Honolulu airport wind
m
/s
0
10
20
30
40
50
Vortex core radius
km
09/14 09/21 09/28 10/05 10/12 10/19 10/26 11/02
0
0.5
1
1.5
Vortex extremum vorticity
R
o
2002
Figure 2: (top panel) 3-day low-pass filtered winds from Honolulu airport (HNL in Fig. 1), (middle
panel) vortex core radius, and (bottom panel) vortex Rossby number, define as the absolute value of the
vortex core extremum vorticity divided by f. Cyclones are shown in thick linesand anticyclones in thin
lines.
We investigate the latter since a majority of vortices were spun up during periods of strong and
steady winds, and that the mean current is weak near the coastand over bathymetry shallower
than 2000 m (Fig. 1). Positive (negative) curl to the northwest (southwest) of Oahu drives
Ekman upwelling (downwelling) which can generate cyclones(anticyclones) (Chavannet al.
(2002)). During the spin-up phase of the strong anticyclone, ∂ζ
∂t
∼ 5.4 × 10−11s−2. Using the
linear vorticity balance (neglecting the beta effect):
∂ζ
∂t
=
curlτ
ρH
(2)
whereρ is density of water and H depth of no motion, taken as 400 m fromobservations at
mooring C1, we obtain a required wind stress curl of∼ 2.2 × 10−5N.m−3, which corresponds
to the average curl over the spin-up period estimated from the airport observations. Therefore
Ekman pumping can explain the vorticity growth of the stronga ticyclone.
The observation of the dominance of anticyclones over cyclones, albeit not statistically sig-
nificant due to the low number of vortices observed, may be simply due to the limited extent of
the observational domain, missing the cyclones to the north.
As conjectured by Sipp and Jacquin (2000), an incompressible inviscid 2D flow with closed
streamlines is prone to centrifugal instability if the signof the absolute vorticityζ + f changes
somewhere in the flow. The absolute vorticity of the strong anticyclone is shown in Fig. 3 at
its peak (on Oct 27, 2002). It does change sign in the core of the vortex, suggesting that the
rapid decay and broadening of the vortex a few days later may be due to centrifugal instability.
Following Kloosterziel et al. (2007), we estimate an upper bound on their growth rate to be
∼3.5 days. Although it takes longer for the instability to affect the entire vortex, this estimate
was derived for a barotropic vortex. For baroclinic vortices, the instability is allowed to grow
faster (R. Kloosterziel, personal communication).
3
18èmeCongrès Français de Mécanique Grenoble, 27-31 août 2007
longitude
la
tit
ud
e
10/27/02
C1
50 cm/s
−159 −158.8 −158.6 −158.4 −158.2 −158 −157.8
20.8
21
21.2
21.4
21.6
21.8
ζ 
+
 f 
[s
−
1 ]
0
1
2
3
4
5
6
7
x 10
−5
Figure 3: Surface currents on Oct 27, 2002 (arrows) and their absolute vorticity ζ + f (color). The zero
contour is shown in black.
3 Vortex Rossby waves
3.1 Description
From March to April 2003, the low-frequency currents variabil ty is dominated by vorticity
waves, as captured by the first mode of a complex EOF analysis of the vorticity in the time do-
main (Fig. 4), which accounted for 54 % of the variance. The waves have a median wavelength
of 110 km, a median propagation direction of 69 degrees ccw from east, and a median period
of 16 days, corresponding to a phase speed of 8 cm/s. Their vertical structure is revealed by the
first EOF mode of the currents observed at A2 (not shown), which accounted for 80 % of the
variance. They are surface-intensified, with an e-folding depth of 225 m and maximum vertical
shear at 80 m, corresponding to5.8 × 10−4s−1 for surface currents of 35 cm/s. The currents
reverse direction at∼800 m, 300 m deeper than the first normal mode reversal depth, and vanish
at the bottom.
A snapshot on Apr 9, 2003 (Fig. 5) shows the spatial structureof the currents and vorticity at
a particular phase of the wave, within the broader context ofmesoscale currents in the Hawaiian
archipelago, as derived from altimetry (Ducet al. (2000)). Vorticity crests of∼0.6 f were
aligned parallel to the island chain, corresponding to alternating northwestward/southeastward
currents of 35 cm/s amplitude, and propagated toward the northeast. A large cyclone of∼100
km radius, which originated in the lee of the Island of Hawaiiin December 2002, was sitting
between 110 and 190 km southwestward of Oahu during spring 2003.
3.2 Dynamics
Due to the eastward component of their phase propagation, these waves cannot be purely plan-
etary Rossby waves. Barotropic and bottom-trapped topographic Rossby waves can have an
eastward phase propagation if the bottom slopes downward tothe north (opposing theβ effect),
but the surface intensified baroclinic modes always have a westward phase propagation, iso-
lating themselves from the topographic effect by moving a node in the horizontal velocity to
the bottom (Rhines (1970)), as observed at A2. The large cyclone radial gradient of vorticity
4
18èmeCongrès Français de Mécanique Grenoble, 27-31 août 2007
re
la
tiv
e 
un
its
0  
0.2
0.4
0.6
0.8
1  
−158.8 −158.4 −158
21
21.2
21.4
21.6
spatial amplitude
de
gr
ee
s
0  
100
200
300
−158.8 −158.4 −158
21
21.2
21.4
21.6
spatial phase
03/05 03/19 04/02 04/16
0
0.2
0.4
0.6
0.8
1
temporal amplitude
re
la
tiv
e 
un
its
03/05 03/19 04/02 04/16
0
5
10
15
20
25
30
temporal phase gradient
pe
rio
d 
[d
ay
s]
2003
Figure 4: Spring 2003 vorticity complex EOF 1: (left panels) spatial and (right panels) temporal struc-
tures of (top panels) amplitude and (bottom panels) phase and phase gradi nt, i.e. wavenumber (left,
arrows) and period (right).
04/09/03
Kauai
Oahu
Maui
Hawaii
50 cm/s
−161 −160 −159 −158 −157 −156 −155
19
19.5
20
20.5
21
21.5
22
ζ 
/ f
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Figure 5: Surface currents on Apr 9, 2003 (arrows) and their vorticitynormalized by f (color) from
altimetry and HFRs. The green arrow shows the direction of phase propagation of the vortex Rossby
waves. The cyclone’s track is shown as a solid black line, with stars every7 days, and a dot for the
center’s location on Apr 9, 2003.
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18èmeCongrès Français de Mécanique Grenoble, 27-31 août 2007
enables the existence of vorticity waves called vortex Rossby waves. Their dispersion relation
is (Montgomery and Kallenbach (1997)):
ω = nΩ +
nζ ′
R(k2 + n2/R2)
(3)
where n is the azimuthal mode number,Ω is the angular velocity of the vortex at the radius R,ζ ’
is the radial gradient of the vortex relative vorticity, andk the radial wavenumber. The frequency
is dominated by the first term (Doppler shift), and so is the radial phase speedω/k, which is
outward for positive k (corresponding to a trailing spiral), explaining the eastward component
of phase propagation seen in the HFRs observations. We infer the vortex characteristics from
an azimuthal average of the observed vortex and evaluate them at the radius going through
the middle of the observational domain of the HFRs. Using the wavenumber obtained by the
complex EOF analysis, projected in the radial direction from the vortex center, equation (3)
yields a period of 30 days for mode number 1 and 15 days for modenumber 2, close to the
periods obtained from the EOF analysis.
4 Conclusions
HFRs observations with 5 km resolution reveal the existence of energetic current variability
on scales typically not resolved by altimetry: submesoscale vortices with radii ranging from 5
to 50 km and vortex Rossby waves with∼100 km wavelength. These oceanic features have
finite Rossby numbers that can reach above one, leading to inertial instability for anticyclonic
vortices. They are surface-intensified and strongly sheared in the vertical. These characteristics
should be taken into account when considering the propagation of inertial and internal waves in
the ocean.
References
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vations of wind variations induced by oceanic islands: implcations for wind-driven ocean
circulation.Can. J. Remote Sensing28(3), 466-474.
Chelton, D.B., deSzoeke, R.A., Schlax, M.G., Naggar, K.E., Siwertz, N. 1998 Geographical
variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr.28, 433-
460.
Ducet, N., Le Traon, P.Y., Reverdin, G. 2000 Global high-resoluti n mapping of ocean circula-
tion from TOPEX/Poseidon and ERS-1 and -2.J. Geophys. Res.105(C8), 19,477-19,498.
Kloosterziel, R.C., Carnevale, G.F., Orlandi, P. 2007 Inertial instability in rotating and stratified
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to spiral bands and intensity changes in hurricanes.Quart. J. Roy. Meteor. Soc.123, 435-465.
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Dynamics1, 273-302.
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Observations of vortices and vortex Rossby waves in the lee of an island

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Observations of vortices and vortex Rossby waves in the lee of an island

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