Antisymmetry of oceanic eddies across the Kuroshio over a shelfbreak

From the analysis of oceanic eddies detected in the drifter trajectories of the Global Drifter Program (GDP) data set, it was found that oceanic eddies are asymmetrically distributed across the Kuroshio in the East China Sea: predominant cyclonic (anticyclonic) eddies are on the western (eastern) sides of Kuroshio. This distribution is confirmed by high-resolution numerical modeling output as well. Most of these eddies are 5~20 km in radius, less than the local first baroclinic deformation radius, thus categorized as submesoscale. The generation mechanism of these submesoscale eddies is speculated to be related to the horizontal velocity shear of the Kuroshio when it flows northeastward along the shelf break in the East China Sea. The budget analysis of eddy kinetic energy shows that both the horizontal shear and vertical buoyancy flux are important energy sources for eddy generation on the two sides of Kuroshio axis. The finding highlights the unique feature of oceanic eddies along the western boundary currents.


Results
The climatological Kuroshio with speed larger than 50 cm s −1 is shown in bold black arrows in the area east to the mainland of China and west to the Ryukyu Islands (Fig. 1). It is derived from 2000-2013 GDP drifter trajectory data. The blue line is the trajectory of drifter ID46956 with cyclonic loops; the red line is the trajectory of drifter ID56756 with anticyclonic loops. It can be clearly seen that a cyclonic eddy and an anticyclonic eddy are present on the western and eastern sides of the Kuroshio, respectively.
Using an eddy detection scheme (ref. 10) with the Lagrangian data, cyclonic and anticyclonic loops (eddies) are detected. They are denoted by blue dots (cyclonic) and red dots (anticyclonic), respectively (Fig. 2a). The thick black line is the main axis of the Kuroshio and defined by the maximum mean velocity values. Grey arrows outside of the Kuroshio region denote that drifter records are insufficient. There are clearly more cyclonic (anticyclonic) eddies are on the western (eastern) side of the Kuroshio.
Along the MPK axis (the solid line), the local region is divided into 12*2 bins which extend out by about 70 km on both sides of the MPK axis. The distance between two adjacent lines perpendicular to the MPK axis is about 20 km. We determined that number of eddies and their size for these bins along the Kuroshio path. In Fig. 2b, the zero line denotes the Kuroshio climatological axis. The bars above (below) the zero line are the numbers of eddies on the western (eastern) side of the Kuroshio. The blue (red) dots mark the mean position of the cyclonic (anticyclonic) eddies. Totally, there are 72 cyclonic eddies and nine anticyclonic eddies on the western side of the MPK; and there are five cyclonic eddies and 41 anticyclonic eddies on the eastern side of the MPK. There are significantly more cyclonic (anticyclonic) eddies in each bin on the western (eastern) side of the MPK, and fewer cyclonic (anticyclonic) eddies on the opposite side. The results show that the characteristics of eddies' distribution in the MPK, namely, polarity-antisymmetric distribution. More cyclonic (anticyclonic) polarity eddies are generated on the western (eastern) side of the Kuroshio. In the eddy size histogram (Fig. 2c), radii of most eddies are about 5-20 km, which is smaller than the first baroclinic deformation radius 50 km in the area 11 .
To further confirm the above results based on the limited drifter data, we employed an Eulerian method 12 to detect eddies from high-resolution modeling output. The results are presented in Fig. 3a. Along the MPK axis region (thick black line) extending out 70 km on both sides, the total 1342 cyclonic eddies and 342 anticyclonic eddies are found on the western side of the MPK; the total 353 cyclonic eddies and 993 anticyclonic eddies on the eastern side of the MPK. Their centers are marked by blue (cyclonic) and red (anticyclonic) dots. The mean currents larger than 50 cms −1 are marked by gray arrows. The results again confirm that the polarity-antisymmetric distribution of oceanic eddies exist across the MPK.
Repeating the same processes used for the drifter data, we obtained statistics for the eddy numbers in 12*2 bins along the Kuroshio path (bins are not shown in Fig. 3a). In the histogram (Fig. 3b), the zero line again denotes the Kuroshio climatological axis. The bars above (below) the zero line stand for numbers of eddies on the western(eastern) side of the Kuroshio. The blue (red) dots are the centers positions of cyclonic (anticyclonic) eddies. There are about one hundred cyclonic (anticyclonic) eddies in the western (eastern) side of the MPK, and fewer cyclonic (anticyclonic) eddies on the opposite side. Again, the results show that the characteristics of eddies' distribution in the MPK, namely, polarity-antisymmetric distribution. In the eddy size histogram (Fig. 3c), we can see that most eddies are sub-mesoscale and their radii are about 5-20 km. Both data sets from different sources, drifters and model output, show similar results. Additionally, the histogram of normalized vorticity shows the skewness of vorticity that the cyclonic vorticity is stronger than the anticyclonic vorticity ( Supplementary Fig. S1).
Using two different methods-Lagrangian (drifter's trajectories) and Euler (model's velocity fields) schemes, we reveal the statistical characteristics of eddy distribution along the main part of the Kuroshio in the East China Sea: polarity-antisymmetric distribution. Most eddies are sub-mesoscale and their radii are peak at 5-20 km. And the cyclonic vorticity is stronger than the anticyclonic vorticity.
For better understanding the phenomenon, we randomly select a line (Fig. 3a) perpendicular to the MPK. The interpolated velocity profiles cross the line show normal distribution in Fig. 4a. On the western (eastern) side of the axis is the positive (negative) horizontal velocity shear, which easily leads to the formation of cyclonic (anticyclonic) eddies, see the schematic figure: Fig. 4b. Potential vorticity (PV) analysis shows that there exists a change in sign of the horizontal gradient of PV along the lines perpendicular to the MPK, see Methods and Supplementary Fig. S2. According to the quasigeostrophic theory (ref. 13), this is the necessary condition for a normal-mode instability with a parallel shear flow: barotropic instability or baroclinic instability when the dominant sign change is mainly due to horizontal shear or vertical shear. So, we speculate that the horizontal shear instability and baroclinic instability could be responsible for the generation of polarity-antisymmetry of oceanic submesoscale eddies across the Kuroshio in the East China Sea.
Based on the eddy kinetic energy (EKE) analysis, the eddy generation mechanism is primarily 14, 15 due to a barotropic instability (HRS > 0), a vertical shear instability (VRS > 0) or a baroclinic instability (VBF > 0), see Methods for the definition and Supplementary Fig. S3 for the annual mean results. The HRS is bigger than the VRS for about one order of magnitude (absolute value) along the MPK. The conversion from mean kinetic energy to eddy kinetic energy is mainly due to the horizontal shear production term. The HRS is positive on the northwest part on the western side and most areas on the eastern side of the Kuroshio axis, which implies the HRS is important for the eddy generation. And the VBF is positive in most areas on the western side of the Kuroshio axis. We integrated the HRS, VRS and VBF along the Kuroshio axis from south to north. The Supplementary Fig. S4 presents the variations of HRS, VRS and VBF across the Kuroshio axis. The annual mean shows that the VBF acts as an energy source and HRS acts as an energy sink for the eddy energy on the western side of the Kuroshio axis, and the HRS acts as a main energy source for the eddy energy on the eastern side.
The EKE budget has strong seasonality. The monthly mean of the EKE analysis is shown in Supplementary  Fig. S5. The positive HRS can be clearly seen in January, April, June and December. Therefore, the HRS also make significant contribution to the eddy generation on the western side of Kuroshio axis with the spatial and temporal variations. Moreover, the previous PV analysis also support this conclusion. So, both the HRS and VBF are important energy sources for eddy generation on the both sides of Kuroshio axis.
To diagnose the scale of energy conversion, we select the December data and a relatively smaller region along the Kuroshio axis (longitude [127°E~129°E] and latitude [26°N~29°N]) to do the wavenumber spectral analyses (see Supplementary Fig. S6). For the relative small scale k = 10 −4 /m (10 km), the VBF power spectra is larger than  the HRS's. And for the relative larger scale k = 10 −5 /m (100 km), the HRS power spectra is larger than the VBF's. It shows that the VBF may play a more important role in the generation of the smaller scale eddies.
It should be noted that ECS have unique features: 1) wide shelf which allows the eddy development on the western side of the Kuroshio. 2) the presence of the Ryuku Islands blocks the influence from open ocean, which is different from the other west boundary currents (e.g. Gulf Stream and East Australia Current). Such antisymmetric phenomenon (polarity-antisymmetry of oceanic submesoscale eddies) and dynamic environment (antisymmetric eddy generation mechanisms) could play an important role in eddy-induced mass and heat transport across the ECS continental shelf.

Methods
Data. The drifter data and high-resolution model output are employed in the study to detect eddies. The historical surface drifter data collected by the Global Drifter Program (GDP; ref. 16) are downloaded from http:// www.aoml.noaa.gov/phod/dac/dacdata.html. Within the study area (24°-32°N and 120°-132°E), 1592 drifters are available from Jul. 1988 to Jun. 2014. However, only 1379 drifters with more than 40 records (longer than 10 days) are used for the eddy detection.

Eddy Detection Schemes.
In this study, we utilize two independent detection methods to study eddies along the MPK. One is Lagrangian eddy detection scheme 10 , and the other is Eulerian eddy detection scheme 12 .
A Lagrangian eddy detection scheme is used to identify loops from the drifters' trajectories. When a drifter is trapped in an eddy, it makes a loop trajectory. To further confirm loops as eddies, a few criteria are used, e.g. the rotational period must be longer than the local inertial period and shorter than the seasonal scale, and there must be at least two consecutive loops with the same polarity in close proximity. This method was successfully applied to the Kuroshio Extension Region (ref. 10).
An Eulerian eddy detection scheme 12 is also used to analyze the surface velocity field from a numerical modeling. This is an eddy detection scheme based on the velocity geometry field, which identifies rotation around an eddy center. For further information about this method, please see ref. 12. This method has been successfully applied to the model outputs 12,18,19 , sea level anomalies-derived geostrophic velocity anomaly data 20,21 , and sea surface temperature-derived thermal-wind velocity data 22 .

PV Analysis. The Ertel potential vorticity (PV) is defined as
e 0 where f is the Coriolis parameter, ẑ is the vertical coordinate, u is the three-dimensional velocity, ρ is the density and ρ 0 is the mean reference density.

Eddy Kinetic Energy Analysis.
To understand the eddy generation mechanism, we estimate the EKE sources through the EKE evolution equation, which is expressed as 14, 15 : = + + + + TT Trans HRS VRS VBF Diffusion, ( 2) where the time variation term The transport terms (Trans) i i i i the vertical shear source i i the vertical buoyancy flux = ′ ′ w b VBF , (9) and the diffusion term i i where u 1 = u, u 2 = v and u 3 = w; u i (i = 1, 2) are the horizontal componets of velocity u j (j = 1, 2, 3); b is the buoyancy and υ i is the vertical mixing. Prime denotes the anomaly with respect to the one-month mean. The over-bar denotes the one-month mean. The horizontal viscosity coefficient is set to zero in the model. The diffusion term is only the vertical mixing.