Divergent Eddy Heat Fluxes in the Kuroshio Extension at 1448-1488E. Part II: Spatiotemporal Variability
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2416 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
Divergent Eddy Heat Fluxes in the Kuroshio Extension at 1448–1488E.
Part II: Spatiotemporal Variability
STUART P. BISHOP
National Center for Atmospheric Research, Boulder, Colorado
(Manuscript received 15 March 2013, in final form 5 July 2013)
ABSTRACT
The Kuroshio Extension System Study (KESS) provided 16 months of observations to quantify divergent
eddy heat flux (DEHF) from a mesoscale-resolving array of current- and pressure-equipped inverted echo
sounders. KESS observations captured a regime shift from a stable to unstable state. There is a distinct dif-
ference in the spatial structure of DEHFs between the two regimes. The stable regime had weak down-
gradient DEHFs. The unstable regime exhibited asymmetry along the mean path with strong downgradient
DEHFs upstream of a mean trough at ;1478E. The spatial structure of DEHFs resulted from episodic me-
soscale processes. The first 6 months were during the stable regime in which fluxes were associated with
eastward-propagating 10–15-day upper meanders. After 6 months, the Kuroshio Extension underwent a re-
gime shift from a stable to unstable state. This regime shift corresponded with a red shift in mesoscale phe-
nomena with the prevalence of ;40-day deep externally generated eddies. DEHF amplitudes more than
quadrupled during the unstable regime. Cold-core ring (CCR) formation, CCR–jet interaction, and coupling
between ;40-day deep eddies were responsible for asymmetry in downgradient fluxes in the mean maps not
observed during the stable regime. The Kuroshio Extension has prominent deep energy associated with
externally generated eddies that interact with the jet to drive some of the biggest DEHF events. These eddies
play an important role in the variability of the jet through eddy–mean flow interactions. The DEHFs that
result from vertical coupling act in accordance with baroclinic instability. The interaction is not growth from
an infinitesimal perturbation, but from the start is a finite-amplitude interaction.
1. Introduction otherwise primarily take a zonal path and act as barriers
to cross-front flow.
The Kuroshio, the western boundary current (WBC)
In Part I [Bishop et al. (2013), hereafter Part I], using
of the Northwest Pacific, plays a critical role in redis-
current- and pressure-equipped inverted echo sounder
tributing heat poleward from the tropics in order to
(CPIES) observations taken during the Kuroshio Exten-
balance the global energy budget. The Kuroshio leaves
sion System Study [KESS; see Part I and Donohue et al.
from the coast at ;358N and flows east as a free jet,
(2010) for details on the KESS experiment], 16-month
called the Kuroshio Extension. The Kuroshio Extension
mean maps of divergent eddy heat fluxes (DEHFs) were
is characterized by vigorous meandering and variability
quantified. There was asymmetry in cross-front DEHFs
on a range of time scales from the mesoscale (from days
along the mean path with strong downgradient fluxes up-
to months) to interannual (Mizuno and White 1983).
stream of a mean trough at ;1478E. The mean vertical
The mesoscale is the most energetic, and satellite al-
structure of the DEHFs had subsurface maxima within the
timetry observations point to the Kuroshio Extension
main thermocline ;400 m. Downgradient parameteriza-
region as one of the regions of highest eddy kinetic en-
tions with constant eddy diffusivities ranging from 800 to
ergy (EKE) in the world’s oceans (Ducet and Le-Traon
1400 m2 s21 fit the vertical structure of the data upstream
2001). Mesoscale eddies drive heat fluxes that transport
of the trough, but did not account for weak upgradient
heat poleward across strong current systems, which
fluxes downstream of the mean trough.
The mesoscale variability in the first 1000 km to the
east of Japan, observed from satellite altimetry, modu-
Corresponding author address: Stuart P. Bishop, National Center lates on decadal time scales between stable and unstable
for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. regimes characterized by minimal and vigorous mean-
E-mail: sbishop@ucar.edu dering, respectively (Qiu and Chen 2005b). Associated
DOI: 10.1175/JPO-D-13-061.1
Ó 2013 American Meteorological SocietyNOVEMBER 2013 BISHOP 2417
with enhanced eddy interaction during unstable regimes is 2. Methods
a weakening of the southern recirculation gyre and sub-
a. Data
sequent reduction in alongfront transport. With the ex-
ception of Hall (1991), who found that the Kuroshio Here, 46 CPIES were deployed in a ;600 km 3
Extension at 1528E had significant energy conversion from 600 km array spanning the Kuroshio Extension jet for
mean to eddy potential energy (EPE) on the anticyclonic 2 years during KESS (Fig. 1). The CPIES array was
side of the current at 350 and 625 dbar, the role of eddy centered in the region of highest surface EKE from
heat fluxes in eddy–mean flow interactions throughout the satellite altimetry (1438–1498E) and spanned the mean-
water column and between meandering regimes remain der envelope from north to south, capturing almost one
unknown in the Kuroshio Extension from observations. full wavelength of the quasi-stationary meander crest–
The KESS experiment fortuitously observed a regime shift trough–crest to the east of Japan (Mizuno and White
from a stable to unstable meandering regime. 1983). The CPIES array had nominal horizontal spacing
In addition to decadal variability in meandering of 88 km, to resolve mesoscale variability. Here, 26 of
states, recent observations from KESS revealed that the CPIES were collocated with Jason-1 altimetry lines
there are mechanisms for cyclogenesis present in the for comparative studies (Park et al. 2012; Bishop et al.
Kuroshio Extension (Greene et al. 2009) that differ from 2012).
what was observed in the Gulf Stream during the Syn- Using observations from the CPIES array, mapped
optic Ocean Prediction Experiment (SYNOP) in the fields of the geostrophic current u, temperature T, and
1980s. Greene et al. (2012) found that during KESS, the density r were determined throughout the water col-
strongest variability in the abyssal ocean was due to umn, which is well documented in Donohue et al. (2010),
30–60-day topographically controlled eddies that had and summarized in Part I. Geostrophic currents de-
formed outside the observational array. The origin of termined with the CPIES express the vertical structure
these eddies was postulated to be the Shatsky Rise as the sum of an equivalent-barotropic internal mode uI
downstream at ;1608E, and model outputs from the and a nearly depth-independent external mode uE
Ocean General Circulation Model for the Earth Simu- measured in the deep ocean. The absolute geostrophic
lator (OFES) support this claim (Greene 2010). In other currents are the summation of the two modes
frequency bands, Tracey et al. (2011) found that ver-
tical coupling between southwestward-propagating u 5 uI 1 uE . (1)
deep eddies and downstream-propagating upper-ocean
meanders resulted in the growth of upper meanders, b. Divergent eddy heat flux
depending upon the phasing between the deep and up-
per ocean. Eddy heat flux is defined as the temporal correlation
The goal of this paper is to determine among the between the geostrophic currents and temperature field
varied mesoscale phenomena observed during KESS and multiplied by the spatially and depth-averaged
the following: density r0 and specific heat at constant pressure Cp
(i) The features responsible for driving the largest r0 Cp u0 T 0 , (2)
DEHFs that make up the 16-month mean spatial
structure in Part I. where an overbar indicates a time mean and a prime
(ii) To characterize the differences in the DEHF spatial indicates a deviation from the time mean (e.g., u0 5
structure between stable and unstable meandering u 2 u); r0 5 1027.5 kg m23 for the KESS observations
regimes. and Cp ’ 4000 J kg21 8C21 for seawater. Equation (2)
(iii) Based on Greene et al. (2012) and Tracey et al. has units of watts per square meter and is commonly
(2011), the role played by deep external eddies in reported in the literature with units of kilowatts per
developing the mean structure of the DEHFs. square meter. Eddy heat flux for the CPIES maps using
The paper is organized as follows. The next section Eq. (1) for the geostrophic currents is
will outline the data and method for determining
DEHFs. Next, the spatiotemporal variability results will u0 T 0 5 u0I T 0 1 u0E T 0 , (3)
be presented, followed by a ring census using satellite
altimetry data. Next, the connection to deep external where multiplication by r0 and Cp is implied.
eddies will be shown with a case study of a CCR forma- The divergent component of the eddy heat flux is the
tion event. Last, the paper will explore eddy energetics dynamical component that plays a role in eddy–mean
and end with a section of discussion and summary. flow interactions, as discussed in Part I and in the2418 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
FIG. 1. (a) KESS observing array. Red diamonds are the locations of 46 CPIES. Color contours are ocean ba-
thymetry from Smith and Sandwell (1997). Black contours are the mean sea surface height (SSH) according to
satellite altimetry taken from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO)
with RIO05 mean dynamic topography over the duration of the KESS experiment (from June 2004 to July 2006). The
bold black contour is representative of the jet axis (2.1-m SSH contour). The dark and light green contours are the
1800 and 2400 cm2 s22 mean EKE contours from 1999 to 2007, respectively. (b) Weekly snapshots of the 2.1-m
contour for first 6 months during the stable regime. (c) As in (b), but for the second 10 months during the unstable
regime.
literature (Cronin and Watts 1996; Jayne and Marotzke the u0E T 0 field was mostly divergent, but that it was
2002; Marshall and Shutts 1981). In Part I, it was de- necessary to remove small rotational effects to correctly
termined that the eddy heat flux associated with the diagnose eddy diffusivity.
internal mode geostrophic currents u0I T 0 is completely
rotational (nondivergent) and proportional to the lat-
3. Spatiotemporal variability in divergent eddy
eral gradient of temperature variance T 02 , as in Marshall
heat flux
and Shutts (1981). Eddy heat flux associated with the
external mode currents u0E T 0 contains the divergence. a. Spatial structure
However, u0E T 0 is not completely rotation free. Ob-
DEHFs [Eq. (4)] in the Kuroshio Extension region
jective analysis (OA) was used to further decompose the
exhibit a different spatial structure depending on whether
eddy heat flux field into divergent and rotational com-
it is in a stable or unstable meandering regime. The hor-
ponents, which uses nondivergent correlation functions
izontal structure of the vertically integrated cross-front
to map the best fit nondivergent vector field to u0E T 0 . The
DEHF between the base of the sea surface mixed layer
divergent component of the eddy heat flux is determined
and deep reference depth
by taking the difference between the full vector field and
the best fit nondivergent field from the OA ð 2H
Ek div
OA
r0 Cp n u0 T 0 dz, (5)
u0 T 0 div 5 u0E T 0 2 u0E T 0 . (4) 2Href
The subscript E has been dropped from the eddy ve- where HEk 5 100 m, Href 5 5300 m, n 5 j$Tj21 $T is the
locity term for the divergent flux for convenience. Re- cross-front unit vector, and $ 5 (›x, ›y) is the horizontal
sults using OA to remove rotation in Part I showed that gradient operator, is presented in Fig. 2 for the 16-month,NOVEMBER 2013 BISHOP 2419
FIG. 2. (a) 16-month, (b) stable, and (c) unstable regime cross-front components of vertically integrated DEHF [Eq. (5)] vectors
superimposed on the depth-averaged baroclinic conversion [color contours; contour interval (CI) 5 0.5 cm2 s23] and mean geopotential
referenced to 5300 m (gray contours; CI 5 1 m2 s22) over each period. The bold gray contour marks the axis of the jet (38.52 m2 s22
geopotential contour, equivalent to where the 128C isotherm crosses the 300-m isobath). (d) Total meridional divergent eddy heat
transport spanning the mean jet path for the 16 month, stable, and unstable meandering regimes.
stable, and unstable regimes. The vertically integrated strong equatorward heat fluxes in Figs. 2a and 2c from
eddy heat flux field resembles the horizontal structure at the passage of a CCR, which cooled the surrounding
all depths because the advecting velocity is independent waters. It was shown in Part I that this feature was as-
of depth and the frontal temperature structure is verti- sociated with convergence of eddy heat fluxes that in-
cally aligned with depth. Superimposed is the depth- duced upwelling.
averaged baroclinic conversion (BCdiv) Mean–eddy energy conversion is different between
meandering regimes. The latitudinal dependence of the
ag div zonally averaged BCdiv across the KESS array in Figs.
BCdiv 5 2 u0 T 0 $T , (6)
Qz 2a–2c is shown in Fig. 2d. On average, BCdiv is positive
along the mean path between 348 and 368N indicating
where a is the effective thermal expansion coefficient es- that the eddies release available potential energy of the
timated from historical hydrography as 1.74 3 1024 8C21, mean flow. During the stable regime, BCdiv peaks at
and g is the acceleration due to gravity. Positive BCdiv is 0.5 3 1023 cm2 s23 at ;358N. In contrast to the stable
an estimate of the energy conversion from mean potential regime, BCdiv is more than two times larger during the
energy (MPE) to EPE with units of square centimeters per unstable regime reaching a maximum 1.25 3 1023 cm2 s23
second cubed. at ;358N. The range of BCdiv between stable and
The spatial structure of the 16-month mean eddy heat unstable meandering regimes along the mean path (0.5–
flux is dominated by the unstable regime where Figs. 2a 1.25 3 1023 cm2 s23) when equated with EKE is suffi-
and 2c have similar features. DEHF is strong and down- cient to produce a depth-averaged eddy velocity of
gradient upstream of the mean trough at ;1478E along the 9–15 cm s21 after one day. Negative conversion is ob-
mean path. served to the south of the jet near ;338N, but only
The stable regime (Fig. 2b), however, is characterized during the unstable regime. This is consistent with up-
by weaker fluxes that are mostly downgradient along the welling and cooling in the region owing to the passage of
mean path. The region of strongest downgradient fluxes a CCR as described above.
in the stable regime shifted upstream compared with
b. Meridional eddy heat transport
the unstable regime. The upstream shift was due to the
presence of low-amplitude frontal meander growth, Differences between the full and divergent 16-month
which will be discussed in an upcoming section. Another mean meridional eddy heat transport was examined in
difference between regimes is that the stable regime did Part I in context of past studies (Qiu and Chen 2005a;
not have any CCRs present. CCR formation events and Volkov et al. 2008; Jayne and Marotzke 2002). In this
their relation to eddy heat flux will too be discussed section, the divergent meridional eddy heat transport
further in an upcoming section. South of the jet there are variability between stable and unstable regimes is2420 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
FIG. 3. (a) Cross-front DEHF time series at 400 m at the five locations in (b). (b) Average spatial structure of DEHF vectors at 400 m
superimposed over the meridional component (color contours; CI 5 275 kW m22), and mean geopotential referenced to 5300 m (gray
contours; CI 5 1 m2 s22) with the bold gray contour marking the axis of the jet (38.52 m2 s22 geopotential contour, equivalent to where the
128C isotherm crosses the 300-m isobath) over the first 6 months (yeardays 152–300). (c)–(e) As in (b), but for values averaged over
yeardays 325–400, 425–550, and 550–580, respectively.
explored. This is a natural question considering that there c. Time series
is enhanced eddy variability during the unstable regime. It
Time series of cross-front DEHF in the Kuroshio
is expected that this would result in larger eddy heat
Extension reveal stark differences in the episodic nature
transport across the Kuroshio Extension front.
between the stable and unstable regimes. Time series of
The total divergent meridional eddy transport was
the cross-front eddy heat flux at 400-m depth are shown
quantified by vertically and zonally integrating the me-
in Fig. 3a for four locations where the mean fluxes were
ridional DEHF
strongest along the mean path plus one location to the
ð x ð 2H south of the jet. The spatial locations are numbered in
e Ek div
tot 5 r0 Cp
Qdiv y 0T0 dz dx, (7) Fig. 3b. Here, 400 m was chosen because this is ap-
xi 2Href proximately the middepth of the thermocline and the
mean fluxes were observed to be strongest at this depth
where xi and xe are the beginning and end longitudes, in Part I.
respectively, that are a function of latitude based on the
1) STABLE REGIME
KESS array grid. Here, Qdiv tot is shown as a function of
latitude across the mean jet path from 34.258 to 36.258N The first six months of observations, from June to
in Fig. 2d for the 16-month, stable, and unstable aver- November 2004, are characterized by the stable regime
aging time periods. The stable and unstable regimes had (Fig. 1b) in which the cross-front eddy heat flux time
tot at ;32.258N that reached a maximum of 0.02 and
Qdiv series has frequent small-amplitude events (Fig. 3a). The
0.06 PW, respectively. There is substantial variability average spatial structure of DEHF at 400-m depth
between meandering regimes with a threefold increase during the stable regime (yeardays 152–300) is pre-
in Qdiv
tot from the stable to unstable meandering regime. sented in Fig. 3b and resembles the vertically integratedNOVEMBER 2013 BISHOP 2421
heat flux structure in Fig. 2b with weak heat fluxes that this interval, there was an abrupt change in the eddy heat
are downgradient. Tracey et al. (2011) showed that this flux time series with eddy heat flux amplitudes more
regime was dominated by small-amplitude, ;50-km peak– than quadrupling (Fig. 3a). The mean spatial structure of
peak lateral displacement, upper-baroclinic frontal waves the eddy heat fluxes during CCRa formation shows
with periods of 10–15 days. These waves traversed the strong poleward fluxes along the mean path just up-
KESS array from west to east with phase speeds of 20– stream of diffluence in the mean streamlines where the
25 km day21 and wavelengths of 200–300 km that ex- ring formed (Fig. 3c). Downstream of this region, there
hibited meander growth at times when coupling to deep are weak upgradient fluxes. To the south of the mean
eddies. Signatures of the growth of these waves are path at the southern extremity of the CCRa formation,
particularly noticeable at sites 1 and 2 in the cross-front there are strong equatorward fluxes, but the mean–eddy
DEHFs between June and mid-August 2004 (yeardays energy conversion (i.e., BCdiv) is only weakly negative
150–225). because the mean lateral temperature gradient is weak
there (Fig. 2c). These fluxes resulted from the coupling
2) UNSTABLE REGIME
of deep eddies with the newly formed ring, which pro-
After yearday 300, the Kuroshio Extension transi- duced the only large event during the site’s five time
tioned from a stable to unstable meandering regime in series (Fig. 3a).
which it remained for the subsequent 10 months of ob- After CCRa completely detached, another CCR
servations (Fig. 1c). During the unstable regime, longer (CCRb) that had formed to the east near the Shatsky
period meanders in the 30–60-day band began to prop- Rise (;1608E) in the previous year propagated into the
agate into the KESS array traveling from west to east southeastern region of the KESS array and interacted
with average periods of 43.5 6 3.7 days, propagation with the jet (illustrated in Figs. 1b and 1c). CCRb was
speeds of 9.6 km day21 (7.8–12.1 km day21), and wave- briefly absorbed by the jet and repinched off to reside to
lengths of 418 6 60 km (Tracey et al. 2011). The origin of the south of the jet for 6 weeks until it was permanently
these longer period meanders is speculated to have re- reabsorbed into the jet. This ring–jet interaction oc-
sulted from two possible mechanisms. One mechanism curred from March to July 2005 (yeardays 425–550) and
is that the jet interacted with a warm-core ring (WCR) at the time series of eddy heat flux events is largest during
the first quasi-stationary meander crest to the east of the latter part of the CCR–jet interaction (yeardays 500–
Japan nearly 50 days prior to the regime shift. The sec- 550). Amplitudes are similar to that during the CCRa
ond mechanism is the jet inflow at the Izu–Ogasawara formation. The mean spatial structure of the eddy heat
Ridge. Qiu and Chen (2005b) argue that the jet shifts to flux during the ring–jet interaction is also very similar to
the south during unstable regimes. When the jet shifts the CCRa formation event with strong poleward fluxes
south, the inflow over the Izu–Ogasawara Ridge flows along the mean path upstream of the trough (Fig. 3d).
through a shallow segment, which leads to large-amplitude Near the end of the 16-month observations, there is
downstream meanders. When the longer period upper a train of deep eddies in the 30–60-day band that prop-
meanders appeared, simultaneously trains of deep, ex- agated into the array from the northeast and traveled to
ternally generated eddies in the 30–60-day band, with the southwest. These deep eddies interacted with the jet
a nominal period of ;40 days, began propagating into causing strong poleward heat fluxes near 358N, 1458E
the KESS array from the east-northeast and turned, (sites 1 and 2) and 348N, 1478E (site 3 and 4) along the
approximately following bathymetry contours, to travel mean path (Fig. 3e).
down the central line from the northeast to the south- The results from this section suggest that there are
west. These eddies interacted with the jet. The origin of varied mesoscale phenomena that produce cross-front
the deep externally generated eddies is thought to be the DEHF events, particularly associated with CCRs. The
Shatsky Rise downstream near 1608E and is discussed in region upstream of the mean trough at 1478E is favored
Greene (2010). for downgradient fluxes. The extrema in the DEHF time
During the unstable regime, there were three major series may be astride the preferred path that deep ex-
events and processes that drove significant cross-front ternal eddies take, following f/h contours where h is the
DEHF along the mean path of the jet: one cold-core ring fluid depth, down the central line of the KESS array
(CCR) formation, CCR–jet interaction, and deep ex- (Greene et al. 2012), and will be discussed in more detail
ternal eddies, which were present throughout the un- in an upcoming section.
stable regime. From late November 2004 to February
d. Cross spectra
2005 (yeardays 325–400), the eastward propagation of
an upper-baroclinic wave was stunted, and the meander The variance-preserving cross spectra between the me-
trough steepened until a CCR formed (CCRa). During ridional external mode currents y E and the temperature2422 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
FIG. 4. Variance-preserving cross spectra between yE and T at the five locations in Fig. 3b for (a) 16-month, (b) stable, and (c) unstable
regimes using the Welch method of spectral estimation with a sample frequency of Fs 5 2 cycles per day (cpd), a segment length of
242 days, a Hanning window, and a 50% overlap.
field (i.e., T ) at 400 m for the same locations in Figs. 3a provided weekly snapshots of the Kuroshio Extension
and 3b provide a useful measure of the spectral content SSH path to do this study. The criterion to count a ring
of the meridional eddy heat fluxes (Bryden 1979; Phillips formation was to manually follow the 2.1-m SSH con-
and Rintoul 2000). Figure 4 displays a shift to lower tour, which is representative of the jet axis and ap-
frequencies in spectral content between the stable and proximately equal to where the 128C isotherm crosses
unstable regimes, which is in agreement with the time the 300-m isobath (Mizuno and White 1983). When
series discussion of the previous two subsections. The a trough developed a closed contour to the south of the
eddy heat flux estimate at each location is retrieved by jet axis and persisted for more than two weeks as
integrating the cross-spectrum a closed contour, this was considered a CCR formation.
ð‘ When a CCR formed, the location of the minimum SSH
r0 Cp y 0E T 0 5 r0 Cp Py dn , (8) within the closed contour was considered to be the for-
T
0 E mation location. Stable and unstable regimes were dis-
tinguished after the work of Qiu and Chen (2010):
where n is the frequency, and PyET is the cross-spectral relatively stable periods were 1993–95 and 2002–05, and
density between y E and T. unstable regimes were 1996–2001 and 2005–07.
During the stable regime, the meridional eddy heat A total of 40 CCRs formed between 1993 and 2007.
flux has peaks at 30 days and shorter (Fig. 4b). During Figure 5a shows the geographic distribution of CCR
the unstable regime, peaks in the meridional eddy heat formations superimposed on topography. There is a gap
flux were more energetic and shifted to periods greater near 1508E where no CCRs formed, which is the mean
than 30 days with energy concentrated around 40 days location of the second quasi-stationary meander crest to
and longer (Fig. 4c). The 16-month meridional eddy the east of Japan.
heat flux spectral content was dominated by variability Within the KESS region (upstream of 1508E), 16
during the unstable regime (Fig. 4a). CCRs formed of which only 1–3 formed during stable
regimes. Figure 5b is a time series from the end of 1992
to mid-2007 of EKE from the AVISO altimetry product
4. Ring census
with RIO05 mean dynamic topography and spatially
In the last section, it was shown that large DEHFs averaged over the KESS array dimensions, 328–388N
are associated with CCR formation. A CCR formation and 1438–1498E. The stable periods were marked as
census was done for a 15-yr period between 1993 and defined in Qiu and Chen (2010), and the times when
2007 at the longitudes of 1408–1658E to see the repre- CCRs formed are marked. One CCR that formed during
sentativeness of the 16 months of KESS observations a stable regime was the ring during KESS and marks the
of stable and unstable regime characteristics in the spa- transition from stable to unstable regimes at the end of
tial structure of DEHF. The AVISO satellite altimetry 2004. Another CCR formed in 1993. It can be argued
product merged with RIO05 mean dynamic topography that this CCR marked the transition from an unstable toNOVEMBER 2013 BISHOP 2423
FIG. 5. (a) CCR formation locations during 1993–2007 for stable (green circles) and unstable
(white circles) regimes superimposed on a mean jet axis according to SSH from the AVISO
updated product and RIO05 mean dynamic topography during 1999–2007 (2.1-m SSH con-
tour). KESS CPIES locations (red diamonds) and bathymetry (CI 5 1000 m) from Smith and
Sandwell (1997) are also given. (b) Surface EKE averaged from 328 to 388N and from 1438 to
1498E from the AVISO satellite altimetry product and RIO05 mean dynamic topography. The
gray horizontal line is the mean EKE over the time series. Gray circles are when CCRs formed
during unstable regimes and black crosses are when CCRs formed during stable regimes within
the KESS array region.
stable regime because EKE levels were well above the jet. Tracey et al. (2011) found that the deep ocean
mean during its formation, but dropped off dramatically, during KESS was populated with westward-translating
staying below the mean until mid-1995. From a closer vi- eddies that were generated external to the KESS array
sual examination of the biweekly paths of the Kuroshio in frequency bands of 3–60 days. They found that upper
Extension in Qiu and Chen (2010), 1993 was a year in meanders and deep eddies jointly intensified when
transition from an unstable to stable regime and still had encountering each other if the phasing was right be-
relatively high levels of EKE (Fig. 5b), which were above tween the deep and upper ocean with the deep eddy
the average. It was not until the end of 1993 that the path offset ;1/ 4 of a wavelength ahead of the upper meander.
was more stable and EKE values dropped, remaining be- The strongest deep eddies, in the most energetic band
low the mean. With that said, only one CCR formed within (30–60 days), propagated down the central line of the
a stable regime in July 2002 (Fig. 5). After that ring KESS array from the northeast to the southwest at
formed, a CCR did not form in the KESS region for nearly propagation speeds of 10–20 km day21 and interacted
3 years from July 2002 to January 2005. The KESS ob- with the upper jet (Greene et al. 2012). These deep eddies
servations during the stable regime were only six months, were absent during the first six months when it was the
but this analysis suggests that it may be representative of stable meandering regime and weak cross-front DEHFs
the previous two years during the stable regime. were observed. Deep eddies began to propagate down
Downstream of 1508E, 24 CCRs formed between 1993 the central line in late October 2004 and were present
and 2007. From Fig. 5, more than half of the rings (16 of thereafter. A train of deep eddies in the 30–60-day band
24 CCRs) that formed downstream are congregated may be responsible for the formation of the CCR near the
around the Shatsky Rise (1558–1618E). This suggests end of 2004, but this merits further research.
that the mechanism of flow–topography interaction may The passage of 30–60-day deep eddies across the jet
promote CCR formation downstream. In the region path is correlated with events in the cross-front DEHF
downstream of 1508E, 10 CCRs formed during stable time series (Fig. 6). After yearday 300, a train of deep
regimes versus 14 that formed during unstable regimes. eddies propagated down the central line and coupled
with the jet. This coupling caused troughs and crests to
grow. The cross-front DEHFs more than quadrupled in
5. Connection to deep external eddies
amplitude along the mean path during the passage of
A mechanism that drives large DEHF is the interaction these deep eddies. Two significant events occurred that
between external eddies and the Kuroshio Extension involved these deep eddies: a CCR formation and a deep2424 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
FIG. 6. (a) Hovm€oller diagram of 30–60-day bandpass-filtered bottom pressure anomaly down the central line. Black and gray contours
are upper 30–60-day bandpass-filtered geopotential anomaly (CI 5 0.5 m2 s22). Green line is the latitude of the jet position at the central
line. (b) Time series of cross-front DEHF along the mean path at 400 m.
eddy–jet coupling event near the end of the 16-month CCR formation (yeardays 300–370). In Fig. 8b, F0I and
observations. The CCR case will now be looked at in F0E have a 40-day periodicity with the deeper leading the
more detail. upper by 8 days. If the interaction is thought of as baro-
clinic instability of the two-layer Phillips model, then the
Cold-core ring formation case study
deep is leading the upper by a phase shift of f 5 2p/5.
Figure 7 shows the DEHF vectors at 400 m from mid- The phase needs to be p . f . 0 for growth, for which
November 2004 to late January 2005 with the 30–60-day f 5 2p/5 is close to optimal growth (f 5 p/5).
bandpass-filtered bottom pressure anomaly and upper The jet–deep eddy interaction is also a heat advection
geopotential anomaly. A wave train of highs and lows in process, which agrees with baroclinic instability (Cronin
the deep propagated from the northeast to the south- and Watts 1996). Associated with the jet–deep eddy
west down the central line of the array during this time. interaction is cold and warm advection during growth,
During the passage of these deep eddies, there was which can be seen from maps of the vertical velocity w
joint development between the deep and upper anom- during the CCR formation (Fig. 9). The vertical velocity
alies. Consequently, the jet axis steepened into a trough. within the thermocline was estimated from variations in
Associated with the trough development were strong the depth of the 128C isotherm Z12 by
downgradient DEHFs within the trough and upstream
from yeardays 325–345. The ring briefly detached and ›Z12
w5 1 u $Z12 , (9)
reattached between yeardays 350 and 365 before it fi- ›t
|ffl{zffl} |fflfflfflfflffl{zfflfflfflfflffl}
nally detached completely. Interestingly though, cross- Tendency Advective
front DEHFs were weak during this reattachment and
detachment process. which has been shown to be consistent with meanders
The interaction of the upper jet and deep eddies in and float observations in the Gulf Stream (Lindstrom
the 30–60-day band has characteristics of baroclinic in- and Watts 1994; Howden 2000). Note that Z12 increases
stability, but is a finite-amplitude interaction from the negatively from the surface downward so that Z12 , 0.
start. Time series of 30–60-day bandpass-filtered upper Between yeardays 320 and 345, there is downwelling
geopotential anomaly referenced to 5300 m F0I and the along the Kuroshio Extension path leading into the
bottom reference geopotential anomaly F0E 5 pb /rb , trough and upwelling leaving the trough. The vertical
where pb is the pressure anomaly at 5300 m and rb is the velocities within the trough are on the order of 6100–
density at 5300 m at location 3 (Fig. 7), are plotted in 150 m day21 (1–2 mm s21), which are weaker than the
Fig. 8. There is growth of both F0I and F0E during the observed vertical velocities during trough events in theNOVEMBER 2013 BISHOP 2425
FIG. 7. Case study of deep external eddy–jet interaction and DEHF during the CCR formation with snapshots every 5 days for yeardays
300–370. Eddy heat flux vectors at 400 m superimposed on 30–60-day bandpass-filtered bottom pressure (color contours), 30–60-day
bandpass-filtered upper geopotential anomaly (bold light and dark gray contours are positive and negative anomalies, respectively; CI 5
1 m2 s22), and geopotential referenced to 5300 m (thin gray contours; CI 5 1 m2 s22) with the bold black contour marking the jet axis
(38.52 m2 s22 geopotential contour).
Gulf Stream (2–3 mm s21; Howden 2000). The downwel- The cold advection within the trough during the CCR
ling within the trough is in precisely the same location as formation is due to the passage of a deep cyclone in the
strong poleward eddy heat fluxes (yeardays 330–340 in Fig. 30–60 band that had a ;2p/5 phase offset leading the
7). It is clear from the 16-month power spectrum of w at upper field. The cyclone advected the Kuroshio Exten-
the four locations in Fig. 9 that the tendency term in Eq. (9) sion front southward, causing the subthermocline layer
is dominated by variability at frequencies higher than to be stretched and further intensified the deep cyclone
1/10 day21 (Fig. 10a). Most of the variance associated with [see Greene et al. (2012) for details of this vertical
the advective term in Eq. (9) is at frequencies lower than coupling mechanism].
1/30 day21 (Fig. 10b). The advection of Z12 is due to deep This CCR formation event is analogous to a cutoff
eddies because the equivalent-barotropic internal mode low-blocking pattern in the jet stream. As the jet axis
currents (i.e., uI) are perfectly aligned with Z12 contours steepened and the trough aspect ratio approached O(1),
upper geopotential anomalies in the 30–60-day band
u $Z12 5 uE $Z12 . (10) were unable to propagate east past the region of large2426 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
FIG. 8. (a) The 16-month time series of 30–60-day bandpass-filtered geopotential anomaly
referenced to 5300 m, F0I , and bottom-referenced geopotential anomaly F0E at location 3 in
Fig. 7. (b) Zoomed-in time series in (a) during the CCR formation.
diffluence. The geopotential anomalies were essentially completely pinched off that upper geopotential anom-
blocked and turned to the south after yearday 305; fol- alies were able to propagate east again. The DEHFs
lowing the deep 30–60-day eddies south into the sub- during this blocking event were strong and down-
tropical gyre (Figs. 7 and 9). It is not until the CCR had gradient within and just upstream of the region of
FIG. 9. Vertical velocities during the CCR formation with 30–60-day bandpass-filtered upper geopotential anomaly (bold light and dark
gray contours are positive and negative anomalies respectively; CI 5 1 m2 s22), and geopotential referenced to 5300 m (thin gray contours;
CI 5 1 m2 s22) with the bold black contour marking the jet axis (38.52 m2 s22 geopotential contour).NOVEMBER 2013 BISHOP 2427
FIG. 10. Variance-preserving power spectrum for w at the four locations in Fig. 9 using the Welch method of
spectral estimation with an Fs 5 2 cpd, a segment length of 256 days, a Hanning window, and a 50% overlap.
(a) Tendency and (b) advective term in Eq. (9).
diffluence. The spatial patterns of DEHF are consistent The zonally averaged EKE, BCdiv, and PKC are
with other studies of blocking patterns and eddy fluxes in shown in Figs. 11a–11c. The EKE is peaked near the
the atmosphere. DEHFs are strong and downgradient mean path of the jet at ;34.58N and more than doubles
upstream of diffluence and may be reinforcing the block between the stable and unstable regimes (Fig. 11a). The
by slowing down the mean flow approaching the dif- BCdiv tends to be larger than the PKC, but they have
fluence (Pierrehumbert 1986; Shutts 1986; Illari and a similar latitudinal structure with positive zones near
Marshall 1983). the mean jet at ;358N. Latitudinal correlation coeff-
icients between the zonally averaged BCdiv and PKC
are 0.85, 0.96, and 0.83 for the 16-month, stable, and
6. Eddy energetics
unstable regimes, respectively.
In the previous section, it was shown that the inter- To explore the temporal variability of BCdiv and PKC,
action of deep external eddies with the Kuroshio Ex- time series of BCdiv0 and PKC0 , where a prime on BCdiv
tension jet have many characteristics of baroclinic and PKC indicates that a time average has not been
instability. Downgradient DEHFs are only one piece of taken, are plotted in Fig. 11d. BCdiv0 and PKC0 were
the puzzle in baroclinic instability. Downgradient DEHFs spatially averaged between 328 and 37.58N and between
are a measure of the eddies drawing eddy potential en- 1438 and 1498E. In estimating PKC0 , it must be stressed
ergy from the mean potential energy of the Kuroshio that only the advective portion of the vertical velocity
Extension jet sloping isopycnals. Vertical eddy heat field u $Z12 was considered. The tendency term vanishes
fluxes are what lead to an increase in EKE, which are for sufficiently long time averaging. This is displayed by
a measure of the energy conversion from EPE to EKE in separating Eq. (9) into mean and eddy terms, multiplying
accordance with baroclinic instability. In this section, by the eddy temperature T 0 and taking a time average
the balance between cross-gradient DEHFs and vertical
eddy heat fluxes (Marshall and Shutts 1981) 0
›Z12
T0 5 0. (12)
ag div
›t
2 u0 T 0 $T 5 agw0 T 0 (11)
Qz
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflffl{zfflfflfflffl} This relation holds because there is a nearly linear re-
BCdiv PKC lationship between T 0 and Z12 (Fig. 12)
will be examined. The latitudinal structure of the zonally T 0 5 mZ12
0
1 b, (13)
averaged BCdiv and PKC in Eq. (11) will be compared
between regimes and their temporal correlation will where m is the slope, and b is the y intercept of the T 0
0
also be quantified. versus Z12 scatterplot. Figure 12a is a plot of the mean2428 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
FIG. 11. (a)–(c) Zonally averaged EKE, BC, and PKC at 400 m for the 16-month, stable, and unstable regimes. (d) Time series of BC0
and advective portion of PKC0 at 400 m that has been spatially averaged over 348–378N and 1438–1498E. (e) Time series of EKE0 at 400 m
with the same spatial averaging as in (d).
temperature at 400 m versus the mean depth of the Figure 11d shows that time series of BCdiv0 and
128C isotherm and Fig. 12b is a similar plot, but of the PKC0 are modestly correlated with a correlation co-
eddy temperature at 400 m versus the eddy depth of efficient of 0.43. However, the major events such as
the 128C isotherm for a given day, yearday 452. On any the CCR formation (yeardays 325–375), CCR–jet in-
given day, there is a 1:1 correspondence between the teraction (yeardays 480–550), and external eddy–jet
slopes of the T at 400 m versus Z12 and T 0 at 400 m interactions (yeardays 550–600) during the unstable
0
versus Z12 , within some small uncertainty to the line regime are highly correlated. The correlation coef-
fit, because the system has nearly parallel isotherms ficient for the unstable regime (yeardays greater
within the main thermocline (Hogg 1986). The y in- than 300) is 0.6. The time means of BCdiv0 and PKC0
tercepts (i.e., b) differ between the eddy and mean are also not statistically different from each other
plots, but are constants for all time. Using the relation with time means of 1.4 6 0.32 (31023) and 1.2 6 0.33
between T 0 and Z12 0
in Eq. (13), it can be shown that (31023) cm2 s23, respectively. During the stable re-
Eq. (12) holds gime, BCdiv0 and PKC0 are correlated during the first
100 days (yeardays 150–250), but there are some PKC0
0
›Z12 › h 0 m 0 i
events that are not related to BCdiv0 from yeardays
T0 5 Z12 Z12 1 b 5 0. (14)
›t ›t 2 250–325.NOVEMBER 2013 BISHOP 2429
0 0
FIG. 12. Scatterplots of (a) T 400 vs Z12 and (b) T400 vs Z12 for yearday 452.
A useful tool is to plot the time-mean midthermocline less than one for the stable and unstable regimes, re-
PKC versus BCdiv as a scatterplot. For wave growth and spectively. This is consistent with the concept that the
decay, the unsteady EPE equation is written as cross-front divergent eddy heat fluxes are within the
wedge of instability during the unstable regime, but not
›EPE during the stable regime. This may explain why some
5 BCdiv 2 PKC , (15)
›t events are uncorrelated during the stable regime (Fig.
11d yeardays 250–325).
where EPE 5 agT 02 /2Qz . Here, Eq. (15) has neglected The temporal changes in EKE0 (Fig. 11e), where
triple correlations and the mean advection of EPE bal- EKE0 5 0.5(u0 2 1 y 0 2) is the EKE before time averaging,
ances the rotational BC (Marshall and Shutts 1981). For are also correlated with events when BCdiv0 and PKC0
wave growth (›EPT/›t . 0), BCdiv must exceed PKC are correlated; such as the three events during the un-
and vice versa for wave decay. The stable (Fig. 13a) and stable regime in the previous paragraph (CCR formation,
unstable (Fig. 13b) regimes show that PKC and BCdiv CCR–jet interaction, and external eddy–jet interaction).
are linearly related with slopes greater than one and The major events during the KESS observations are
FIG. 13. Scatterplot of PKC vs BCdiv at 400-m depth between 348 and 378N for (a) stable and (b) unstable regimes
with a linear regression fit (solid black line). The dashed line is the 1:1 line.2430 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 43
associated with a mean–eddy energy conversion, from KESS array central line, cross-front DEHFs were weaker
MPE to EPE, and further conversion to EKE in ac- than during the unstable regime and no CCR formed. In
cordance with baroclinic instability. fact, prior to this, a CCR did not form from July 2002 to
December 2004 during the stable regime as observed
from the ring census. However, whether there were deep
7. Discussion and summary
external eddies during this time period is unknown and
DEHFs in the Kuroshio Extension arise from varied outside of the time interval of the available data.
mesoscale processes. The dominant features responsible The results from this study suggest there are distinct
for the largest observed variability during KESS were differences in the mean structure of DEHFs between
deep externally generated topographically controlled stable and unstable meandering regimes, and between
eddies and CCRs. Growth of upper meanders associated the features that drive that structure. During the stable
with deep externally generated upstream-propagating regime, DEHFs were weak and mostly downgradient.
eddies in various frequency bands (5–60 days) (Greene The dominant cross-steam DEHFs arose from 10–15-day
et al. 2012; Tracey et al. 2011) arises in accordance with upper meanders, which grew upstream near 1458N. The
baroclinic instability; downgradient DEHFs were asso- suppression of CCR formation during stable regimes
ciated with the growth of meanders, which release MPE suggests that processes observed during the first six
of the mean jet to the eddies. This process is different months of the KESS observations during the stable
from the canonical view of baroclinic instability. The regime are characteristic of the previous two years.
SYNOP experiment revealed observationally for the The unstable regime was characterized by a red shift
first time the importance of vertical coupling between in the spectral content, the presence of CCRs, and
deep eddies and the Gulf Stream variability (Watts et al. asymmetry in downgradient DEHFs along the mean
1995; Howden 2000; Savidge and Bane 1999). Cronin path. CCRs are the features responsible for the asym-
and Watts (1996) observed cross-front eddy heat fluxes metry in downgradient DEHFs. Cross-front DEHFs
from trough events that were associated with vertical were strong and downgradient upstream of a mean
coupling between deep eddies and the Gulf Stream. trough in the along streamflow. Vertical coupling be-
These deep eddies spun up in place owing to lateral tween deep eddies and the upper jet, combined with two
excursions of the Gulf Stream, which can easily generate CCR formations produced the majority of the variance
deep vorticity between 0.1 and 0.2f. in the unstable regime.
As was discussed in Greene et al. (2009), due to Eddy energetics analysis points to the DEHFs as
a more shallow thermocline and thicker subthermocline playing a role in eddy–mean flow interactions through
layer than in the Gulf Stream, cyclogenesis by baroclinic energy conversion. Time series of BCdiv0 (proportional
stretching from lateral excursions of the Kuroshio Ex- to cross-front DEHFs) were correlated with vertical
tension jet is weak and insufficient to explain variability heat fluxes (PKC0 ) during strong events, suggesting on
observed during KESS. At the extrema of lateral ex- average that eddies are releasing available potential
cursions, baroclinic stretching can generate vorticity of energy from the mean baroclinic jet to drive the kinetic
0.1–0.12f. Deep external eddies with relative vorticity in energy of the eddies. This gives a firm ground on which
excess of 0.1f were observed to interact with the jet; to interpret the DEHFs in terms of dynamics and vari-
driving strong cross-front DEHFs. When the phasing is ability in EKE.
right, this vertical coupling between deep externally As with any observational study in the ocean, many
generated eddies and the upper-ocean jet, with the more years of data are needed to accurately access
deep leading the upper as in Phillips-like baroclinic in- long-term trends and convergence of statistics. The
stability, is associated with the growth of upper mean- cross spectra of the meridional eddy heat fluxes for the
ders. A case study of these 30–60-day deep eddies 16 months show that there is still a lot of unresolved
showed that they can shift the jet south; forming steep energy at long periods. For convergence of statistics,
meander troughs that sometimes form in place and a time series long enough such that the energy at the
pinch off CCRs. Some of the strongest DEHFs were longest periods vanishes would be needed. However,
associated with this process. It begs the question whether this study showed that there are varied mesoscale
the Kuroshio Extension between 1438 and 1498E is ca- processes that drive DEHF and that there are distinct
pable of locally generating its own deep vorticity through differences between stable and unstable regimes.
internal processes or whether external features needed to
form extreme trough events such as a ring formation. Acknowledgments. I thank D. Randolph Watts for our
Otherwise, during the stable regime, when there was an many thoughtful discussions that improved this manu-
absence of 30–60-day deep eddies traveling down the script. This manuscript was also improved by the helpfulNOVEMBER 2013 BISHOP 2431
comments of two anonymous reviewers. I thank the Howden, S. D., 2000: The three-dimensional secondary circulation
captains and crews of the R/V Thompson, R/V Revelle, in developing Gulf Stream meanders. J. Phys. Oceanogr., 30,
888–915.
and R/V Melville. The CPIES were successfully de-
Illari, L., and J. C. Marshall, 1983: On the interpretation of eddy
veloped, deployed, and recovered by G. Chaplin and fluxes during a blocking episode. J. Atmos. Sci., 40, 2232–2242.
E. Sousa with the assistance of Gary Savoy and Cathy Jayne, S. R., and J. Marotzke, 2002: The oceanic eddy heat trans-
Cipolla at the URI Equipment Development Labora- port. J. Phys. Oceanogr., 32, 3328–3345.
tory. I also thank Karen Tracey, Kathy Donohue, and Lindstrom, S. S., and D. R. Watts, 1994: Vertical motion in the Gulf
Stream near 688W. J. Phys. Oceanogr., 24, 2321–2333.
Andy Greene for help in processing and mapping the
Marshall, J., and G. Shutts, 1981: A note on rotational and di-
CPIES data. This work was supported by the U.S. Na- vergent eddy fluxes. J. Phys. Oceanogr., 11, 1677–1679.
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and OCE08-51246. ability in the Kuroshio Current system. J. Phys. Oceanogr., 13,
1847–1867.
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