Dynamics of Eddies in the Ocean

Abstract

In this chapter we apply Lagrangian methods to study mesoscale eddies, rotating coherent features which exist almost everywhere in the ocean. In the first part we focus on a mesoscale anticyclonic eddy that has been sampled in the R/V Professor Gagarinskiy cruise (June–July 2012) in the area to the east off the Kuril Islands in the North Western subarctic Pacific. Lagrangian approach is applied to study formation, structure, and evolution of this feature called the eddy A and of its parent eddy B using a simulation with synthetic tracers advected by the AVISO velocity field. In the second part the output from an eddy-resolved multilayered circulation model is used to analyze the vertical structure of simulated deep-sea eddies in the Japan Sea constrained by a bottom topography. We focus on Lagrangian analysis of ACEs, generated in the model in a typical year approximately at the place of the mooring and the hydrographic sections, where such features have been regularly observed. Using a quasi-3D computation of the FTLEs and displacements for a large number of synthetic tracers in each depth layer, we show that the simulated feature evolves from the eddy, that does not reach the surface in summer, into the feature reaching the surface in fall.

6.1 Eddies in the Ocean

Eddies, which are energetic, swirling, robust, and long-lived features, have been found almost everywhere in the ocean [7, 10, 11]. Their size varies with latitude, region, bottom topography, and other factors. They can be characterized by a horizontal scale to be submesoscale eddies with the diameter < 10–20 km and mesoscale eddies with larger diameters. Most of the kinetic energy of ocean circulation is contained in eddies. Eddies are important also because they transport momentum, heat, nutrients and provide mixing of waters with different properties.

Mesoscale eddies are particularly apparent along the paths of intense western boundary ocean current like the Gulf Stream, the Kuroshio, the Agulhas Current, and others. They also can be found in the mid-ocean both at the high and low latitudes. There are a number of mechanisms of generation of such eddies. A class of eddies, which are formed from the western boundary currents through the pinch-off of meanders, are called “rings“ [22]. They may transport water of the parent current over thousands of kilometers and may exist for a few years. Free eddies in the mid-ocean are formed mainly due to a baroclinic instability of surface currents. Some eddies can be generated by winds or cooling at the sea surface. Flows over sea mounts and other prominent features of the sea floor, past islands, and capes generate topographically constrained eddies. Submesoscale and mesoscale eddies are often formed near the coasts and over the continental shelf due to a side friction and the corresponding instability.

By their shape and structure, the vortex features can be divided into monopole, dipole (mushroom currents), tripole, and multipole ones. Eddies with the same polarity can form vortex pairs exchanging by water with each other. Satellite images sometimes show vortex streets with submesoscale or mesoscale eddies moving over a trench, along the continental shelf or a coastline. The vortex configuration may be rather complex, for example, with a large mesoscale eddy or a ring surrounded by smaller-size eddies with opposite polarity. A specific class of eddies with the scale smaller than 30 km (typically around 10–20 km) are frequently observed at the sea surface both from satellites and space shuttles. They are spiral in form, overwhelmingly rotate cyclonically, and extend to 300 m below the surface. They have been observed in the regions where currents produce no or a little horizontal stress [41].

As to the vertical structure, most of the large-scale eddies are cone-like “bags” of water reaching sometimes a few km downward. Moreover, there are intrathermoclinic eddies which are manifested not at the sea surface but inside the thermocline [9, 12, 14, 43, 45]. There also exist hetons which are eddies of opposite polarity one over another [42, 44, 45]. The eddies move either being advected by a background current or due to interaction with other eddies, streamers, intrusions, etc. The β-effect is not large enough to influence mesoscale eddies. However, it is sufficiently large to drag mesoscale eddies and rings asymptotically to the west in the northern hemisphere. Decay and death of eddies may be caused by different reasons: small-scale turbulent diffusion, radiation of planetary waves, interaction with background currents, interaction with other eddies, etc.

Before the satellite era it was difficult to detect eddies in the mid-ocean, just like to search for a needle in a haystack. Sparse distribution of in situ measurements limited our knowledge of eddies in the ocean. As to rings around the Gulf Stream and Kuroshio, they have been known to sailors and fishermen long ago. Mesoscale eddies in the mid-ocean have been discovered only in the late 1960s. Satellite SST sensors and altimeters changed the situation cardinally. The current satellite missions provide global real-time data for measurements of SST and the SSH above the ocean rest state with high precision and high space and time resolution.

The FTLE diagnostic enables to identify boundaries of mesoscale eddies in a given velocity field. As an example, we demonstrate in Fig. 6.1a, a NASA satellite image of the sea color in the Oyashio–Kuroshio frontal zone in the North Western Pacific Ocean to the east of the Hokkaido Island (Japan) in May 2009 during the period of a spring bloom of phytoplankton. The phytoplankton becomes concentrated along the boundaries of the mesoscale eddy tracing out the motion of water. Computing altimetry-based daily FTLEs and other Lagrangian indicators we were able to trace out the birth and history of that eddy. It was found to be a Kuroshio warm-core ring to be split off the Kuroshio Extension Current, the powerful eastward jet, that transports warm subtropical waters approximately along 35^∘ N–37^∘ N latitudes (see Figs. 4.1 and 4.3). That ring slowly migrated to the north and reached to May 2009 its place in Fig. 6.1. It should be stressed that its core contains mainly warm and salty Kuroshio water that is strongly different from more cold and fresh ambient Oyashio water. The boundaries of such rings are known to be attractive for phyto- and zooplankton, and, therefore, fish and other marine organisms may accumulate there for feeding [28, 29, 33].

Fig. 6.1

(a ) NASA image of ocean color illustrating spring bloom of phytoplankton near Hokkaido (Japan) in May 2009. Phytoplankton concentrates along the boundaries of the mesoscale eddy tracing out the vortex motion of water. (b ) Combined forward- and backward-in-time (Λ ₊ and Λ ₋, respectively) FTLE maps computed with the AVISO velocity field superimposed by arrows. Λ is in days⁻¹. Track of the Argo float no. 2900946, launched at the western periphery of that eddy on January 27, 2009, is shown by the green stars from the launching date up to the end of its mission, on January 16, 2010. The largest star marks its position on May 21, 2009 and the other ones show its positions each 5 days before and after that date. The crosses and triangles mark “instantaneous” hyperbolic and elliptic stationary points on May 21, 2009, respectively

In simulation we distribute a large number of tracers in the area and advect them forward and backward in time for 30 days in the AVISO velocity field starting from May 21, 2009. We integrate Eq. (4.1) for each pair of initially closed tracers and compute the FTLE in accordance with (4.12). Those forward- and backward-in-time values, Λ ₊ and Λ ₋, then are coded by color and plotted together on the geographic map in Fig. 6.1b. We recall that the physical meaning of the FTLE is the rate of divergence of initially closed particles for a given period of time.

Track of the Argo float no. 2900946 (for reference, see [ARGODB]), launched at the western periphery of that ring on January 27, 2009, is shown in Fig. 6.1b by the green stars. The float has been captured by the ring and provided valuable information on vertical profiles of temperature, density, and salinity up to January 16, 2010, the end of its mission. That Hokkaido ring was a quasistationary feature staying practically at the same place for a year but gradually decreasing in diameter. Large mesoscale ACEs appear often to the east off the Hokkaido Island. Sometimes they are Kuroshio rings, and sometimes not.

6.2 Altimetry-Based Lagrangian Analysis of Formation, Structure, Evolution, and Splitting of Mesoscale Kuril Eddies

6.2.1 Mesoscale Kuril Eddies

Mesoscale ACEs have been regularly observed on the oceanic side off the Kuril Islands near the Bussol’ Strait in the North Western subarctic Pacific to the south of the Kamchatka Peninsula (see Fig. 6.2) [1, 5, 6, 19, 35–39, 52]. It is the deepest Kuril strait through which water inflows to the Okhotsk Sea and outflows from it [34, 50]. Such eddies are observed in this area every year in the SSH-anomaly field and infrared satellite images. They are one of the most energetic and prominent features in the western subarctic gyre in the North Pacific which require detailed study of their hydrographic structure and understanding the processes of their origin, dynamics, transformation, and decay. They are supposed to control significantly transport of the East Kamchatka and Oyashio currents and modify the properties of these source waters of the North Pacific Intermediate Water [52].

Fig. 6.2

The mesoscale Bussol’ ACE A in the SSH field by satellite altimetry. Locations of the CTD transect in the R/V Professor Gagarinskiy cruise in 2012 are shown by the white circles with some stations numbered. “Instantaneous” elliptic and hyperbolic points in the AVISO velocity field, to be present in the area on June 25, 2012, are indicated by the triangles and crosses, respectively

Extensive hydrographic observations of those eddies [6, 19, 35–39, 52], especially in the last decade of the twentieth century, allowed to sample their vertical structure, dynamics, and kinematics. They are observed along the entire chain of the Kuril Islands from the Hokkaido Island up to the Kamchatka Peninsula and thus control water exchange at the western boundary of the subarctic gyre. However, the origin of those eddies is not clear. Are they advected from the north (south) or do they form locally?

Based on satellite altimetry data and current meter moorings, it was demonstrated that the eddies in the southern and central Kuril area move typically to the northeast while the eddies in the northern Kurils area move southwestward [15]. At least, some Kuril ACEs are believed to be modifications of warm-core Kuroshio rings that moved northward for several years. One of them, called WCR86B, split off from the Kuroshio Extension in 1986 and reached the Bussol’ Strait at the latitude 46. 5^∘ N in September 1990 when it has been sampled [19, 35, 37, 53]. This eddy moved along the Kuril–Kamchatka Trench and disappeared in the end of 1991. Even so far away from its origin, it had a warm and high-salinity core in the upper layer and a secondary low salinity core at the intermediate depth (250–600 m). Other large warm-core eddy has been sampled off the Bussol’ Strait in summer of 1995 [52]. This eddy can be tracked back in time when it was a Kuroshio warm-core ring with its center located around 46. 5^∘ N and 146. 5^∘ E in summer of 1994, and then it moved northeastward with decreasing size for a year and disappeared in February 1996. During the evolution of the WCR86B, its warm core has been observed to shrink with subsequent formation and enlargement of its secondary cold core. This allowed to propose that during its evolution in the subarctic waters the Kuroshio warm-core rings eventually change their structure to cold-core rings typical for Kuril eddies [19]. Another suggestion is that the Kuril ACEs are formed locally by intrusion of cold fresh water outflow from the Okhotsk Sea [37, 52]. Even if an eddy was not formed locally but migrated from the south, an interaction with the Okhotsk Sea water outflow should impact significantly on its water mass structure and dynamics.

It was shown that regular appearance of large ACEs to the east off the Kuril Islands are important for water dynamics and its modification in the area. Approaching the coast, such a migrating eddy could block the coastal flow and thus intensify the offshore branches of the East Kamchatka and Oyashio currents. The Kuril eddies affect the distributions and vertical fluxes of the dissolved oxygen, nutrients, and dissolved inorganic carbon in the Oyashio region and thus affect the plankton bloom there with an impact on marine biota. Using in situ observations and satellite data, it has been found that boundaries of the Kuril eddies were composed of productive coastal Oyashio water which was wrapped around the eddy core creating a high productive belt [18].

A recent interest to those eddies has been motivated by the accident at the FNPP in March 2011. Measurements of the¹³⁷Cs and¹³⁴Cs radioactivity along with hydrographic sampling of a number of mesoscale eddies in the broad area to the east off Japan and the Kuril Islands have been conducted in the R/V Professor Gagarinskiy cruise (June 13–July 10, 2012) [4] (see Chap. 7). In particular, a cold-core Kuril ACE, called the eddy A in [4], has been sampled in the end of June 2012 with the center at that time at 46. 19^∘ N, 154. 33^∘ E. It was suggested that ACEs could accumulate water with high concentration of radioisotopes because of convergence and subduction processes and then transport this water while migrating northward. Even if it was actually proved for the Kuroshio warm-core rings it might not be so for the Kuril eddies. The observed concentrations of¹³⁴Cs and¹³⁷Cs across the eddy A at different depths have not exceeded the background level in the ocean [4].

The eddies consist of a core and a periphery. The core is a uniform water mass which conserves for a while its physicochemical properties. Periphery is a water mass involved in a vortex motion around the eddy center. Strong potential vorticity gradient at the core boundary allows fluid particles in theory to enter and leave the core only due to diffusion. The eddy periphery deforms and exchanges water with its surroundings much more effectively than the core. However, peripheral water masses may differ by its properties from ambient waters. In spite of the tremendous progress in studying oceanic eddies, mechanisms of their formation, propagation, and decay are not well understood and may be different in different regions. Even eddy identification is not a simple task (see, e.g., [7, 8, 17]). Water exchange between the eddy core and the surroundings is also not well understood. It is important as well to know how eddies gain, retain, and release water.

We focus in this section on the Kuril anticyclonic eddy A or the Bussol’ eddy, that has been sampled in the cruise R/V Professor Gagarinskiy in June 2012, and on its parent eddy B. We apply a Lagrangian approach to study formation, structure, evolution, splitting, and merging of those eddies based on the AVISO velocity field. To be more concrete we will deal with the following issues:

• Identification of eddies and their boundaries in the altimetric velocity field.

• Documenting deformation, interaction, and splitting of eddies.

• Tracking water exchange between eddies and its surroundings: how and when they gain, retain, and release water.

• Tracking the origin of core and peripheral waters: which waters fill the eddy core and its periphery and how they do that.

• How fluid parcels leave the eddy core and its periphery and where they are headed for.

Our simulations are verified in part by tracks of available surface drifters and Argo floats [GDP, ARGO].

6.2.2 CTD Sampling of the Bussol’ Eddy A

The cruise of the R/V Professor Gagarinskiy was conducted by the Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences in June and July 2012 with the aim to collect data on distribution of Fukushima-derived¹³⁴Cs and¹³⁷Cs isotopes in some areas of the Japan and Okhotsk seas and the adjacent area in the North Western Pacific [4]. Part of the cruise included observations in the area of the central Kuril Islands with a CTD transect from the Okhotsk Sea to the Pacific Ocean through the Bussol’ Strait crossing a large mesoscale Bussol’ eddy A (Fig. 6.2). That eddy was identified by satellite altimetry data. Its center and boundaries have been identified with the help of Lagrangian diagnostic maps operationally computed and transmitted to the board by radio. Special attention was paid to cross the eddy as close as possible to its center. With this aim a few stations have been done at the expected location of its center obtained by computing the corresponding elliptic point in the AVISO velocity field. Observations were implemented from surface down to the depth of 2000 m with the CTD SBE 911plus equipped with two sets of temperature and conductivity sensors, as well as sensors of dissolved oxygen, turbidity, and fluorescence. Observations across the Bussol’ Strait have been done by the CTD SBE 19plus down to 600 m. In total, 13 stations down to 2000 m and 8 stations down to 600 m have been done in June 23–27, 2012 for the following analysis of the eddy structure.

The SSH field in Fig. 6.2 shows that the eddy A located east of the Bussol’ Strait and the Simushir Island is the most prominent and intense dynamic feature in the region with the positive SSH in its center exceeding 40 cm. Distribution of water properties along the CTD transect from the Okhotsk Sea to the Pacific Ocean, crossing the eddy center, is presented in Fig. 6.3. The eddy had a well-developed vertically uniform core located between 100 and 700 m. Eddy core water had lower temperature and salinity and higher concentration of dissolved oxygen and turbidity. The core water mass characteristics are similar to the Okhotsk Sea water. However, the core of the eddy has much lower stratification than the Okhotsk Sea water which is clearly seen at the distribution of potential vorticity (Fig. 6.3f). This suggests that water has been well mixed vertically by convergence process in the eddy core and possible convection in winter. High content of dissolved oxygen may prove intense vertical convective mixing in this layer.

Fig. 6.3

Vertical distribution of (a ) potential temperature, (b ) salinity, (c ) potential density anomaly, (d ) dissolved oxygen, (e ) turbidity, and (f ) potential vorticity along the section from station 35 in the Okhotsk Sea (left) to station 55 in the Pacific Ocean (right) across the Bussol’ eddy A by CTD observations in the R/V Professor Gagarinskiy cruise from June 23 to 27, 2012. The numbers of stations are indicated on the top of each panel

The uplifting of the isolines in the upper layer of the eddy indicates a relative cyclonic shear above 200 m depth (Figs. 6.3 and 6.4). Thus we may suggest that the eddy has its main core located between 100 and 700 m, and the upper part of toroidal shape is clearly seen in the surface layer above 40 m (Fig. 6.4c). There is a colder and higher salinity and thus higher density water in the center of the eddy and lower density water at its periphery in the layer above 200 m. This water has a little different properties than that in the Okhotsk Sea. It has a little higher temperature and salinity.

Fig. 6.4

The same as in Fig. 6.3 but in the upper 100 m layer

It is interesting to note that in the center of the eddy surface water has much higher turbidity up to 0.25–0.33 FTU (Fig. 6.4e). It could be caused by plankton activity. There is a high chlorophyll content (a high fluorescence) at the layer corresponding to seasonal pycnocline with maximum at 10–20 m in the Okhotsk Sea and the Bussol’ Strait, around 20–40 m in the eddy, and 30–50 m in the Pacific to the south (Fig. 6.4f). It results in the high content of dissolved oxygen in this layer because of photosynthesis (Fig. 6.4d). However, there is no indication to high plankton activity in the center of the eddy where a high turbidity water has been observed. It is not clear why this water has a much higher turbidity than surrounding waters. One of the mechanisms could be convergence of water in the center of the eddy. Thus, water in the eddy center has been trapped there for a long time, while water at its periphery is a result of involvement of surrounding water masses, and its lifetime in the eddy is much shorter. In the next section we will examine the water exchange in the eddy using the Lagrangian approach.

6.2.3 Lagrangian Analysis of the Sampled Bussol’ Eddy A

6.2.3.1 Evolution and Metamorphoses of the Kuril Eddies in 2012

In this section we focus on the first two issues mentioned in Sect. 6.2.1. Lagrangian tools are applied to identify a Kuril anticyclone, which we call the eddy B, and to document its deformation, splitting, and genetic coupling with the eddy A that has been sampled in the R/V Professor Gagarinskiy cruise in the end of June 2012. To do that let’s compute backward-in-time Lagrangian drift maps and plot particle’s displacements D (4.2) for 30 days in the AVISO velocity field. Such a map on February 1, 2012 in Fig. 6.5a clearly shows the eddy B with the elliptic point at its center 46. 3^∘ N, 153. 3^∘ E. The boundary of that eddy can be identified approximately as a closed curve with the maximal (locally) gradient of D that passes through the hyperbolic point at 47. 2^∘ N, 153. 7^∘ E. That curve separates the waters, involved in the rotational motion around the vortex center, from ambient waters. Displacements of fluid particles for the former ones are much smaller than for the particles outside the eddy (“dark” waters in Fig. 6.5a). The spirality of the eddy B on the map is a typical feature for drift maps with eddies (see, e.g., [26, 27]). The spirality just means that water parcels inside an eddy rotate with different angular velocities, and the distances, D, between final and initial positions of particles differ in bands of different color.

Fig. 6.5

Lagrangian drift maps show evolution, deformation, and splitting of the eddy B that gave birth to the eddy A. The displacement of particles D (in km), computed for a month backward in time from the day indicated in each panel, are coded by nuances of the grey color. “Instantaneous” elliptic and hyperbolic points, to be present in the area on fixed days, are indicated by triangles and crosses, respectively. Tracks of two drifters are shown by full circles for 2 days before the day indicated with the size of the circles increasing in time. Tracks of the Argo float no. 4900939, approached the eddy B in the end of March, are shown by the stars. The largest star corresponds to the day indicated and the other ones show its location each 5 days before and after that date. The colored squares are patches with tracers whose deformation is shown

In the beginning of 2012, the Kuril mesoscale ACE B was observed near the coast of the Simushir Island to the east of the Bussol’ Strait (Fig. 6.5a). The East Kamchatka Current rounds it from the east and south (the black band around that eddy in Fig. 6.5a). The eddy B started to deform in February due to an intensification of the East Kamchatka Current and development of a meander. Its elliptic point has been shifted during a month to the south by almost 1^∘ (Fig. 6.5b). An elliptic point at 46^∘ N, 153^∘ E appeared on April 14 at the center of the newly formed eddy A. Simultaneously a hyperbolic point appeared at 46. 2^∘ N, 152. 5^∘ E between the centers of the eddies B and A (Fig. 6.5d). The blue patch, placed on March 24 at the center of the eddy B (Fig. 6.5c), stretched strongly to the middle of April due to splitting of the eddy B and formation of the eddy A. The blue filament encircles the young eddy A around its elliptic point.

Splitting of the eddy B and birth of the eddy A in the middle of April are confirmed by a track of the drifter no. 42949 coming from the north (the string with the red circles in Fig. 6.5d–f). The circles increase in size through time and show locations of the drifter every 6 h, i.e., Fig. 6.5d shows a fragment of the drifter’s trajectory from 0:00 GMT on April 12 to 0:00 GMT on April 14. It encircles the eddy A anticyclonically in the second half of April confirming our simulation (Fig. 6.5e, f). Water from the core of the eddy B formed the core of the eddy A (look at evolution of the blue patch). The periphery of the eddy A consists mainly of waters from the north (look at evolution of the red patch in Fig. 6.5c placed on March 24 to the north of the eddy B).

The eddies A and B form an anticyclonic vortex pair with a hyperbolic point arising just after splitting of the eddy B. It is shown on April 14 by the cross in Fig. 6.5e at 46. 2^∘ N, 152. 5^∘ E. By definition, each hyperbolic point has contracting (stable manifold ) and expanding (unstable manifold ) directions along which water parcels in the course of time converge to it and diverge away from it, respectively. Figure 6.6 with the drifter tracks clarifies the role of hyperbolic points and their manifolds in organizing oceanic flows around.

Fig. 6.6

(a )–(e ) Lagrangian drift maps show evolution of the eddy A till the sampling days in the end of June 2012. Tracks of the drifters are indicated by full circles for 2 days before the day indicated with the size of the circles increasing in time. Tracks of the Argo float no. 4900939, approached the eddy A in the end of April and be trapped by it from May to October, are shown by the stars. The largest star corresponds to the day indicated and the other ones show its location each 5 days before and after that date. (f ) Combined Lyapunov map of forward (Λ ₊) and backward-in-time (Λ ₋) FTLEs on June 25, 2012. Λ is in days⁻¹. Locations and numbers of sampling stations across the eddy A are shown

Two drifters nos. 42949 and 42970 in Fig. 6.6a on April 28 approach that point, located now at 46^∘ N, 152. 3^∘ E, along its stable manifolds from the south and north. When approaching the hyperbolic point, they slow down (compare Figs. 6.5e, f and 6.6a, b) because of the presence of a dynamical saddle trap in a vicinity of hyperbolic (saddle) points [51] (see Sect. 2.2.3). Then the drifters begin to move away from the hyperbolic point to the west and east in the course of time along the unstable manifolds of that point (Fig. 6.6b–d on April 29, May 2 and 3). The southern drifter no. 42970 moves away from the hyperbolic point and eventually enters the Okhotsk Sea via the Bussol’ Strait, whereas the northern one no. 42949 encircles the eddy A once more before going away. The eddy A progressively grows in size during April, May, and June gaining surrounding water (look at the red filaments encircling its core in Fig. 6.6a–d). The eddy A has practically a circular form by the days of sampling with the elliptic point on June 24 at 46. 3^∘ N, 154. 3^∘ E and the size of ≃ 140 × 135 km in the meridional and zonal directions, respectively.

The FTLE maps provide a complementary tool to visualize eddies and confirm the results obtained with the D maps. We compute forward-in-time (Λ ₊) and backward-in-time (Λ ₋) FTLE fields by the method presented in Sect. 4.3.1 [27] for 15 days in the future and in the past, respectively, starting from June 25. The combined map in Fig. 6.6f clearly shows the eddy A as a closed region bounded by black “ridges” intersecting at two hyperbolic points. The FTLE “ridges” are locations of particles on a given day with maximal (locally) values of the FTLE. Particles on both sides of a “ridge” diverge maximally in the future and in the past. It means that the water parcels on one side of the “ridge” are involved in the vortex motion around an elliptic point, whereas the ones on the other side move away from the eddy. Thus, intersecting “ridges” on the FTLE map approximate the eddy boundary.

In Fig. 6.7 snapshots of the SSH field on March 24, April 18, and April 24, 2012 show, respectively, the eddy B with the center at 45. 7^∘ N, 152. 3^∘ E (the left panel), its splitting (the central panel) and formation of the eddy A with the center at 45. 6^∘ N, 153. 3^∘ E (the right panel).

Fig. 6.7

Snapshots of the SSH field on March 24, April 18, and April 24, 2012 which show, respectively, the eddy B with the center at 45. 7^∘ N, 152. 3^∘ E (the left panel), its splitting (the central panel), and formation of the eddy A with the center at 45. 6^∘ N, 153. 3^∘ E (the right panel)

6.2.3.2 Structure of the Kuril Eddies A and B and Water Exchange

Using specific backward-in-time Lagrangian maps we study here horizontal structure of the eddy A, the origin of its core, and peripheral waters and how they are situated within that eddy. The other task, connected with the first one, is to track by means of forward-in-time Lagrangian maps by which ways fluid parcels leave the parent eddy B to form the core of the newborn eddy A and its periphery.

The tracking maps in Fig. 6.8 show in the logarithmic scale where the tracers placed on the material line along the R/V Professor Gagarinskiy cruise track, crossing the eddy A, have been found for the period in the past from June 25 to April 11, 2012 (Fig. 6.8a) and for a much longer period from June 25, 2012 to the day of the accident at the FNPP, March 11, 2011 (Fig. 6.8b). The map in Fig. 6.8a, computed throughout life of the eddy A, confirms that some tracers of that line came to their locations on the dates of sampling from the Okhotsk Sea, whereas the most part of them has been advected by the East Kamchatka Current from the north. The longer history of the eddy A waters in Fig. 6.8b shows a larger area visited by the eddy A tracers for 15 months after the Fukushima accident. This map demonstrates that the risk of a radioactive contamination of the eddy A surface waters is minimal. Observed¹³⁷Cs and¹³⁴Cs concentrations inside the eddy A in the R/V Professor Gagarinskiy cruise in the end of June 2012 have been found to be at the background level not only in surface waters but also in the depth [4].

Fig. 6.8

Simulated backward-in-time tracking maps for the tracers distributed on the material line along the R/V Professor Gagarinskiy cruise track crossing the eddy A. The maps show where those tracers have been from (a ) June 25 to April 11, 2012 and from (b ) June 25, 2012 to the day of the accident at the Fukushima Nuclear Power Plant, March 11, 2011. The density of tracers, ν, is in the logarithmic scale. Radioactivity sign shows location of the FNPP

A large number of tracers were uniformly distributed in the box [153^∘ E–155. 5^∘ E; 45. 5^∘ N–47^∘ N], including the eddy A, and integrated backward in time from June 25 to April 11, 2012 in the regional AVISO velocity field. Coding by different colors the particles which entered the area through its geographical borders for that period of time, we plot in Fig. 6.9a the drift Lagrangian map that shows where water masses, constituting that eddy, came from. Yellow color means that the corresponding particles entered the box shown in Fig. 6.9a through its western boundary, green, blue, and red ones—through its eastern, northern, and southern boundaries, respectively. “Grey” particles in the inner core of the eddy A are those ones which were present in the box for the integration period.

Fig. 6.9

(a ) Backward-in-time drift map shows where the waters of the eddy A came from for the integration period from June 25 to April 11: yellow—from the west, green—the east, blue—the north, red—the south, grey color codes the waters that have been in the box during all that period in the past. The absolute displacement, D, for the grey particles is in km. (b ) Vortex rings revealed by the entrance-time map. The day T, when particles entered the eddy A in the past, is coded by the grey color. (c ) The rotation map shows how many times particles have rotated around the eddy center from April 11 to June 25, 2012. (d ) Dependence of the entrance day T on longitude λ of particles distributed initially on the zonal material line along 46. 3^∘ N

To reveal horizontal structure of the eddy A we fix the dates in the past when the particles entered the box. The box shown in Fig. 6.9 is seeded with a large number of tracers on June 25. The advection equations (4.1) are solved backward in time from June 25 to April 11. The days, when tracers entered the box, T, are fixed and coded by nuances of the grey color. The entrance-time map in Fig. 6.9b shows how many days ago a tracer with given initial coordinates crossed one of the box boundaries. The colored patch at the eddy center means that the corresponding tracers have been there before April 11. The rings in Fig. 6.9b of different color mean that the eddy has captured and wound water by portions. It is an analogue of tree rings. The eddy core can be identified there as a boundary of contrast colors. The rotation map in Fig. 6.9c shows how many times the particles rotated around the eddy center from April 11 to June 25, 2012. This plot has a ring-like structure as well.

The process of winding of water onto the eddy by portions becomes evident with the plot of dependence of some particle’s characteristics inside the eddy on their coordinate. We solve advection equations (4.1) backward in time from June 25 to April 11 for the particles distributed initially on the zonal material line crossing the eddy along 46. 3^∘ N and fix the day, T, when particles with given longitudes λ entered the vortex area (Fig. 6.9d). The plot in Fig. 6.9d consists of a hierarchy of segments with “quantized” portions of the zonal material line with close entrance dates. As expected, the entrance dates for particles in the outer parts of each segment are older than for those in the inner parts. The straight line with the maximal values of T in Fig. 6.9d corresponds to the patches in the inner core in Fig. 6.9a, b.

A direct evidence of subsequent winding of surrounding water onto the eddy A is provided by backward-in-time evolution of a material line placed along the R/V Professor Gagarinskiy cruise track crossing the eddy A. The particles of that line have been integrated backward in time from June 25 (Fig. 6.10a). Figure 6.10b demonstrates how the eddy has wound water for June. The process of splitting of the eddy B is clearly seen in Fig. 6.10c plotted on April 28. Figures 6.5 and 6.6 illustrate a genetic connection between the eddies B and A.

Fig. 6.10

Backward-in-time evolution of a material line placed along the R/V Professor Gagarinskiy cruise track crossing the eddy A in the end of June 2012

In order to track the origin of the eddy A by a complementary way we compute forward-in-time Lagrangian maps for the eddy B. The box with that eddy in Fig. 6.11a is seeded with a large number of tracers which are integrated forward in time from March 25 to June 25, 2012. Coding by different colors the particles which left the box through its geographical borders for that period of time, we get the drift Lagrangian map that shows where water masses of the eddy headed for (Fig. 6.11a). Yellow color means that the corresponding particles crossed the western boundary, green, blue, and red ones—the eastern, northern, and southern boundaries, respectively. The “grey” particles in the inner core are those ones which did not leave the box for the integration period. “Green” waters in the eddy B core is a source of eddy A waters. In fact, the eddy B split into two parts, as shown in Figs. 6.5 and 6.6, with the eastern part to be formed initially by the core waters of the eddy B. Then surrounding waters wound onto that split part of the eddy B by portions as shown in Figs. 6.9 and 6.10 and eventually formed the eddy A which has been sampled in the end of June 2012.

Fig. 6.11

(a ) Forward-in-time drift map shows where the waters of the eddy B headed for over the integration period: yellow—to the west, green—to the east, blue—to the north, red—to the south, and grey color codes the waters that did not leave the box for that period of time. (b ) The residence time map. The day T, when the particles left the vortex area, is coded by the grey color

Two 0. 25^∘× 0. 25^∘-size patches with tracers were placed on June 25, 2012 at the locations of stations 45 (blue patch in Fig. 6.12a) and 49 (red patch in Fig. 6.12a) at a periphery of the eddy A and near its center, respectively, and advected backward in time. Tracking the history of those patches, we see that on March 10 the red tracers were concentrated mainly in the eddy B (Fig. 6.12d). However, some of them originated from the Okhotsk Sea and the East Kamchatka Current. On April 28, they were compactly distributed among two eddies, inside a remnant of the eddy B and in the newborn eddy A (Fig. 6.12c). As to the blue tracers, they were distributed over a large area, mainly to the east of the Kuril Islands with a small “tail” in the Okhotsk Sea. Figure 6.12b plotted on June 1 shows the red tracers distributed in the eddy A core and the blue ones winding around that core.

Fig. 6.12

Backward-in-time evolution of the patches with tracers distributed at the locations of (a ) station 45 at a periphery of the eddy A and (b ) of station 49 near its center in the R/V Professor Gagarinskiy cruise

6.2.4 Vertical Profiles of Temperature and Salinity by the Argo Floats

The eddy A was born as a result of splitting of another Kuril eddy B in the area east of the central Kuril Islands which happened in middle April of 2012. We have observed evolution of the eddy B since the beginning of 2012 (Fig. 6.5). In early February the eddy had a circular form around 165–170 km in diameter and was located just to the east of the Simushir Island. Then during February–March the eddy was moving to the southwest by around 100 km down to the area off the Bussol’ Strait. We explain this transition of the eddy by an intensification of the East Kamchatka Current. Its branch is clearly seen in the D field as an area with the highest displacement’s values just upstream of the eddy (Fig. 6.5a and b). The SSH snapshots in Fig. 6.7 clearly show the eddy B, its splitting and formation of the eddy A in accordance with Fig. 6.5c, e, and f.

It may be suggested that the impact of the East Kamchatka Current resulted in changes of the eddy form from a circular to elliptic one and beginning of its splitting in the middle of April. The splitting of mesoscale eddies could be traced by satellite altimetry charts or infrared images. However, Lagrangian drift and FTLE maps show more detailed pattern of this process in space and time. They demonstrate clear boundaries between the eddies identifying water particles belonging to one or another vortices (Figs. 6.6 and 6.9). The eddy B splitting and formation of the eddy A from its southeastern part were also confirmed by satellite-tracked drifters and Argo floats. After its formation, the newborn eddy A was quickly increasing in size by involving surrounding water and was moving to the north. By the end of June when its CTD sampling was implemented by the R/V Professor Gagarinskiy , the eddy was located just to the east of the Simushir Island with its center at 46. 3^∘ N, 154. 3^∘ E and had a size of ≃ 140 × 135 km (Fig. 6.6e, f).

The center of the eddy A was identified in the cruise to be at the point 46. 197^∘ N, 154. 334^∘ E on June 26, 2012. It is station 50 (see Table 7.1 in the end of Chap. 7). The corresponding simulated elliptic point of that eddy had coordinates 46. 3^∘ N, 154. 3^∘ E on the same days (see Fig. 6.6e, f). The simulated and measured locations of the center of the eddy A coincide with the accuracy of 7–10 km. As to comparison of simulated and measured boundaries of the eddy A, it follows from the potential vorticity plot in Fig. 6.4 that the eddy core was located on June 25–26, 2012 between stations 46 (46. 5^∘ N, 153. 5^∘ E) and 53 (46^∘ N, 155^∘ E). Positive SSH values in Fig. 6.2 were located between the points with coordinates 45. 7^∘ N and 47^∘ N and 153. 5^∘ E and 155^∘ E. The boundary of the eddy core on the simulated D map in Fig. 6.6e can be identified as a closed outer contour with a maximal local gradient of D between 45. 7^∘ N and 47^∘ N and between 153. 3^∘ E and 155. 2^∘ E. The black “ridge” on the combined Lyapunov map in Fig. 6.6f, delineating approximately the boundary of the eddy core, crosses the cruise transect between stations 53 and 54. It delineates approximately the same boundary of the eddy A as that on the potential vorticity plot, D and SSH maps.

Previous studies of the eddies in the area off the central Kuril Islands [5, 15, 19] suggested that their migration to the northeast was caused by the mean flow. This corresponds to our observations of the drift of the eddies B and A. Southwestward motion of the eddy B and northeastward motion of the eddy A represent seasonal variations of the mean flow in the area east of the Kuril Islands, e.g., the winter intensification of the East Kamchatka Current and the summer intensification of the flow from the subarctic front area to the north.

The Argo float no. 4900939 was deployed by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) on August 31, 2009 at the western Aleutian Islands. Its parking depth was around 500 m and a frequency of profiling was 5 days [ARGODB]. The float travelled through the Bering Sea more than 2 years and then came out to the North Western Pacific with the East Kamchatka Current. Drifting to the southwest along the Kuril Islands, the float has been captured by the eddy B at its northeastern periphery in the end of March 2012. Profiles of temperature and salinity taken by the float in March represent a typical winter modification of North Western Pacific Subarctic water mass structure with cold mixed upper layer (0–150 m) of 0.5–0.6 ^∘C and 33.09–33.14 PSU and warm intermediate layer between 200 and 400 m with temperature increasing up to 3.5–3.7 ^∘C (Fig. 6.13).

Fig. 6.13

(Left) Vertical profiles of temperature T and salinity S obtained by the Argo float no. 4900939 in the vicinity of the eddy B on March 18, 23, and 28, 2012. T and S profiles by CTD observations of R/V Professor Gagarinskiy on June 25 at the periphery of the eddy A (st. 45) are shown for a comparison. (Right) The velocity field on March 23 and the floats locations on March 18, 23, and 28 in the vicinity of the eddy B

When the float came into the area of the eddy B on March 28, 2012, its profiles were changed presenting more colder and lower salinity water between 200 and 450 m. Similar profiles were obtained at the southern and western periphery of the eddy on April 2, 7, and 12 when the float left the eddy and drifted into the Okhotsk Sea (Fig. 6.14). These profiles coincide with the T and S profiles obtained on June 25, 2012 by the CTD observations of R/V Professor Gagarinskiy at the periphery of the eddy A at station 45 (Figs. 6.3, 6.4, 6.13, and 6.14). The comparison suggests that the float has not entered the core of the eddy B, but it was travelling along its periphery clockwise. Slight difference of profiles for April 7 and 12 from those of March 28, April 2 at station 45, and similarity of the first ones with the profile taken in the mixed water area in the Bussol’ Strait on April 17 may suggest that the float was leaving the eddy that time.

Fig. 6.14

(Left) Vertical profiles of temperature T and salinity S obtained by the Argo float no. 4900939 at the periphery of the eddy B on April 2, 7, 12, and 17, 2012. T and S profiles by CTD observations of R/V Professor Gagarinskiy on June 25 at the periphery of the eddy A (st. 45) are shown for a comparison. (Right) The velocity field on April 12 and locations on April 2, 7, 12, and 17 of the float moving clockwise around the center of the eddy B

By May 12, 2012, the float has entered the eddy A from the northwest (Fig. 6.15). It seems that this time the float finally came into the core of the eddy and was trapped there by October. Vertical profiles of T and S inside the eddy and in the area around the Kuril Islands are similar and demonstrate mixed cold and low salinity water of 1.2–1.8 ^∘C and 33.1–33.5 PSU between 100 and 450 m. The same vertical structure was also observed by the CTD profiling close to the Kuril Islands by R/V Professor Gagarinskiy on June 25 (st. 44). Similarity of the profiles and the fact that the float has penetrated into the center of the eddy (not just taken along its periphery) may suggest an intrusion of the mixed Okhotsk Sea water into the core of the eddy A. The float has circulated in the core of the eddy A for the next 4.5 months. It sent the last signal on October 4, 2012 from the center of the eddy after more than 3 years of operation. All 27 profiles, taken in the eddy since May 17, show no changes in the structure of the eddy core and demonstrate good coincidence with the ship CTD observations taken in the end of June (Fig. 6.16). The fact that the float was trapped inside the eddy core suggests its uniform vertical structure by the depth 500 m, otherwise the float could hardly stay inside the eddy for such a long time. It is difficult to estimate currents inside the eddy by float track data. We may estimate a time of full rotation of the eddy to be 6–7 days which is close to the period of the float profiling (5 days). So we do not see a loop-like track of the float in Fig. 6.16. Instead, one can note a northward expansion of the float track which is caused by the northward drift of the eddy over May–October period.

Fig. 6.15

(Left) Vertical profiles of temperature T and salinity S obtained by the Argo float no. 4900939 at the periphery of the eddy A on May 2, 7, and 12, 2012. T and S profiles by CTD observations of R/V Professor Gagarinskiy on June 24 at the periphery of the eddy A (st. 44) are shown for a comparison. (Right) The velocity field on May 7 and the floats locations on May 2, 7, and 12 in the vicinity of the eddy A

Fig. 6.16

(Left) Accumulated vertical profiles of temperature T and salinity S obtained by the Argo float no. 4900939 in the eddy A from May 17 to October 4, 2012. T and S profiles by CTD observations of R/V Professor Gagarinskiy on June 26 in the core of the eddy A (st. 49) are shown for a comparison. (Right) The velocity field on May 17 and locations of the float trapped by the eddy A for the period from May 17 to October 4

Observations by the float show a similarity of vertical structure of the eddies B and A. Thus, along with our Lagrangian simulations, this confirms a genetic connection of the studied eddies. The fact that the float came into the center of the eddy A and a similarity of its profiles, taken along the Kuril Islands with those in the core of the eddy, suggest an intrusion of the Okhotsk Sea water into the eddy A during or just after its separation from eddy B in late April. This mechanism of the Kuril eddies formation was discussed by Yasuda et al. [52].

The CTD observations across the eddy A by the R/V Professor Gagarinskiy in June 26–27, 2012 showed its vertical structure to be quite typical for the Kuril eddies with a core of relatively low temperature and low salinity water at the intermediate depth [5, 39, 52]. This very uniform core of the eddy A with an extremely low potential vorticity layer had a very large vertical size extending from 100 down to 700 m (Fig. 6.3). As to the other mesoscale ACEs in the ocean, the uniform core forms during eddy evolution by entrainment of surrounding water and mixing inside the eddy core (see, e.g., [22]). This process of vertically uniform core formation takes time from a few months to a few years. So it is hardly possible that this core, containing such a large volume of well mixed water, was formed in the eddy A since the eddy formation in middle April during 2 months before the CTD sampling. It looks more probable that this core is a remnant of the eddy B. Lagrangian simulations, presented in the section, were started in the beginning of 2012 and continued 6 months by the period of ship sampling. However, we expect the age of this deep core of the eddies B and A to be much longer because the eddy B was presented in the area long before our observations. In fact, altimetric observation and simulation showed that it was born in the area in June 2009 with the elliptic point to be at that time at 45^∘ N, 153^∘ E.

Based on the CTD observations, we may suggest that the core of the eddy A consisted of its deep part located between 100 and 700 m and upper part above 100 m (Figs. 6.3 and 6.4). While the deep core was quite isolated from surrounding water, the upper core was influenced by intrusions of surface water from the adjacent areas. Lagrangian simulations provide tracing the origin of the entrained water. First, we confirm that the main part of water, forming the core of the eddy A, came from the eddy B (Figs. 6.5 and 6.6). Entrainment of surrounding water into the eddy occurred by portions and was associated with development of streamers transported water mainly from the north and winding onto the eddy forming its spiral-like structure (Figs. 6.9 and 6.10). While water at the eddy periphery was renewing quickly, water at the very central part of the eddy was quite isolated. It was captured inside the eddy for a long time and originated from the eddy B which was influenced, in turn, by the Okhotsk Sea water (Figs. 6.8, 6.12 and 6.10). This may explain different properties of water in the center of the eddy observed by the CTD sampling, in particular, a high turbidity in the upper layer (Fig. 6.4). Water at the eddy periphery originated mostly from the East Kamchatka Current and Okhotsk Sea (Figs. 6.8 and 6.12). There was no water entrainment into the eddy from the southern areas during the study period. This result is very important to estimate a role of this eddy in transporting water contaminated by radionuclides after the Fukushima accident in March 2011. Our results confirmed that even the eddy had a slightly increased concentrations of radiocesium isotopes in June 2012 it was not a result of direct water transport from Tohoku area while it could be a result of atmospheric transport and deposition [4].

6.3 Lagrangian Analysis of the Vertical Structure of Numerically Simulated Eddies in the Japan Sea

6.3.1 Topographically Constrained Frontal Eddies in the Japan Basin

When simulating mean near-surface circulation in the Japan Sea based on multi-year altimetry data in Chap. 5, we have found a quasi-permanent anticyclonic feature to the north of the central Polar Front, labeled as AC in the averaged AVISO velocity field in Fig. 5.2 This anticyclonic eddy with the center at about 41. 3^∘ N, 134^∘ E has been shown to play an important role in existence there a “forbidden” zone where northward transport of water has not been observed for the period of integration from 1993 to 2015. Topographically constrained anticyclonic eddies have been really regularly observed there [24, 47, 48].

As part of an international cooperative program “Circulation Research of the East Asian Marginal Seas” (CREAMS), long-term moored current measurements have been carried out at seven sites in the Japan Basin. One of the moorings, M3, was deployed at 41. 5^∘ N and 134. 3^∘ E where the Japan Basin is 3500 m deep. It was equipped with three current meters at about 1000, 2000, and 3000 m depths which made the measurements for 3 years, from August 1993 to July 1996, with the data sampling period of 1 h. The current meter data of 3-year duration have shown that deep-sea ACEs with the orbital speeds of the order of 0.1 m/s occurred every year in the deep layers [47]. Available time series of SST images and World Ocean Circulation Experiment (WOCE) drifter tracks well correlated to that finding. The currents at 1000, 2000, 3000 m have been found [47] to be highly coherent throughout the observational period. They have observed intensification of the current in fall and winter. The eddies observed in the Japan Basin did not exhibit any definite direction of propagation. It has been noted in [47] that the effect of the bottom geometry may be important. In fact, the eddy currents were observed only at M3, but not in the rim area of the Basin at M1, M2, M4, M6, and M7 stations [47]. During the oceanographic CTD-hydrochemical survey in summer 1999 [48, 49], the mesoscale ACE with the center approximately at the site of the M3 mooring has been found in temperature, salinity, dissolved oxygen, and NO₃ sections along 134^∘ E and 41. 25^∘ N.

In this section we use the output from the eddy-resolved multilayered circulation Marine Hydrophysical Institute Model (MHIM) [40] to analyze from a Lagrangian perspective, the vertical structure of simulated deep-sea ACEs in the Japan Basin constrained by bottom topography. We focus on the ACE, generated in the MHIM approximately at the place of the M3 mooring [47] and the hydrographic sections [48, 49], where such eddies have been regularly observed in different years (1993–1997, 1999–2001).

Lagrangian tools have been shown in the preceding section to be useful in identifying 2D structure of eddies, their cores and boundaries, and pathways by which they gain and expel water (see also [2, 21, 26, 27, 30, 31, 46]). The challenge is in identification of the vertical structure of eddies. In order to quantify properties of the 3D eddy structure (for example, the volume of eddies), it is often the eddy’s surface edges are simply extended to a given depth along the vertical. It is well known, however, that most eddies do not have a cylinder-like form. Moreover, the intriguing problem is changed in the structure of eddies at different depths in the course of time.

The analysis in this section will be performed using two Lagrangian indicators, the FTLE [23] and displacements for a large number of tracers [25, 30, 32]. The Lagrangian diagnostics we use seem to be more appropriate to identify eddies than the commonly used techniques, because FTLE and drift maps are imprints of history of water mass involved in the vortex motion whereas vorticity, the Okubo–Weiss parameter, and similar indicators are “instantaneous” snapshots. That is why one can see eddies more clearly on the Lagrangian maps. We will show how our modeled ACE evolves from the eddy without any signs of rotation motion at the sea surface in summer into a one reaching the surface in fall. In order to demonstrate that we implement a quasi-3D computation of those Lagrangian indicators. We use the velocity field from the output of the MHIM and compute the Lagrangian maps of the FTLE and particle’s displacements in each model layer.

Quasi-3D Lagrangian approach has been applied recently [3] for diagnostics of 3D LCSs around a particular CE pinched off from a Benguela upwelling front. Three-dimensional LCSs were extracted as “ridges” of the calculated fields of the FTLE obtained from an output of the Regional Ocean Modelling System (ROMS). They have been found [3] to be quasi-vertical surfaces. Another eddy feature, a ring of the Loop Current in the Gulf of Mexico has been studied [46] by the similar method, using the data-assimilating HYbrid Coordinate Ocean Model (HYCOM). Those authors have studied the location of relevant transport barriers during the formation of the Eddy “Franklin” in 2010 at several depths from the surface down to 200 m.

6.3.2 Regional Circulation Marine Hydrophysical Institute Model

We introduce briefly the quasi-isopycnic layered MHIM [20, 40] with a free surface boundary condition incorporating the horizontally inhomogeneous upper mixed layer. The model is based on a system of primitive equations integrated within each quasi-isopycnic layer. All layers are assumed to be horizontally inhomogeneous, however, the density in each thermocline layer changes within the limits determined a priori by the prescribed basic stratification.

It is assumed that the layers may outcrop. The layer outcropping is similar to the isopycnal model applied by Hogan and Hurlburt [13] to the Japan Sea. The interfaces of the inner model layers can climb to the upper mixed layer in the frontal zones. The horizontally inhomogeneous upper mixed layer model includes a parametrization of turbulent heat, salt and momentum fluxes, drift current in that layer, entrainment and subduction processes at the bottom of the layer [20, 40]. The basic equations for momentum, temperature, and salinity in the upper mixed layer are similar to the vertically integrated equations for inner layers of the model. The commonly used convective adjustment scheme is applied to simulate vertical convection. According to our previous studies [27], the MHIM successfully simulates the mesoscale eddy dynamics, interaction between eddies over the shelf edge and steep continental slope of the Japan Basin, as well as, mesoscale eddies and currents, mixing and transport of water masses in the Peter the Great Bay in the Japan Sea [31].

The numerical experiment with the MHIM is focused in this section on simulation of the mesoscale circulation over the deep Japan Basin, its continental slope and shelf during summer and fall. The model domain is the closed sea area [39^∘ N–44^∘ N; 129^∘ E–139^∘ E] with the horizontal resolution 2.5 km [27].

Both biharmonic and harmonic viscosities are used in the momentum equation of the sea circulation model, and only harmonic horizontal diffusion is used in the equation for the temperature and salinity transfer. The coefficients of biharmonic horizontal viscosity and diffusion are set to be constant in space. The coefficient of harmonic horizontal viscosity is a constant in space only during model spin up. After the model spin up, the harmonic horizontal viscosity is taken into account only near the boundary of the model domain. The model is integrated in time from June to November to simulate relatively stable mesoscale ACEs in the Japan Basin. As horizontal boundary conditions, we set zero values for the current velocity and its second derivative along a normal to the boundary, as well as zero values for the first derivatives of temperature and salinity. Therefore, we consider a closed model domain. Due to the realistic initial conditions, basic density stratification below seasonal pycnocline and main features of the large-scale cyclonic circulation over the Japan Basin do not significantly change during this 6 months period. Formation and evolution of the mesoscale eddies in the area studied (Fig. 6.17b) do not substantially depend on the boundary conditions in the model domain from early summer to late fall.

Fig. 6.17

The bottom topography in (a ) the northern part of the Japan Sea and (b ) the studied area

The model has ten quasi-isopycnic layers with the first one to be a horizontally inhomogeneous upper mixed layer. The first nine layers are located inside the main pycnocline with the lower boundary of the ninth layer to be the lower boundary of the main pycnocline which is not deeper than 250 m in the area studied. The lower tenth layer includes deep and bottom waters of the Japan Sea. The realistic bottom topography (Fig. 6.17), obtained from ETOPO2 (2-Minute Gridded Global Relief Data), is one of the most important factors in simulation of the large-scale and mesoscale circulations.

The initial conditions for summer isopycnal interfaces in the model layers, temperature, and salinity distribution include only large-scale features of the model variables. They have been taken from oceanographic survey in 1999 [48, 49] with a substantial smoothing. After smoothing, there were no any mesoscale structures in the initial conditions. The MHIM has been integrated with the time step of 4 m in from the initial condition under realistic meteorological situations. The first month with June meteorological conditions is a time interval of the model spin up. The wind stress, short wave radiation, near-surface air temperature, humidity, and wind speed have been taken from daily mean National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) Reanalysis. The heat fluxes at the sea surface, being depended on the mixed layer temperature and meteorological characteristics, are calculated in the model.

In the model spin up (30 days), the coefficients of quasi-isopycnic biharmonic viscosity, harmonic viscosity, and diffusion used in the momentum and heat/salt transfer equations have been decreased correspondingly from 10¹⁷ cm⁴ s⁻¹, 10⁷ cm² s⁻¹, and 0. 4 ⋅ 10⁷ cm² s⁻¹ to 2 ⋅ 10¹⁶ cm⁴ s⁻¹, 0. 5 ⋅ 10⁶ cm² s⁻¹, and 0. 2 ⋅ 10⁶ cm² s⁻¹. After spin up, the harmonic viscosity is applied only in two grid lines adjacent to the contour of the model domain with the coefficient 0. 5 ⋅ 10⁶ cm² s⁻¹. In other offshore grid points, this coefficient is set to be zero and only biharmonic viscosity in the momentum equations is taken into account with the coefficient 2 ⋅ 10¹⁶ cm⁴ s⁻¹. The coefficient of temperature, salinity diffusion is 0. 2 ⋅ 10⁶ cm² s⁻¹ in all the grid points after spin up. We basically simulate the nonlinear large-scale and mesoscale circulation over the Japan Basin, continental slope, and shelf taking into account daily mean external atmospheric forcing from July 1 to December 1. The numerical experiments with minimized coefficients of the horizontal and vertical viscosity show intensive mesoscale dynamics. In particular, they demonstrate variability of the mesoscale ACEs and CEs over the shelf, the shelf break and base of the continental slope, and in the central deep area of the Japan Basin as well. The anticyclonic eddies, generated over the shelf break and continental slope, move usually downstream with prevailing phase velocity of about 6–8 cm/s [27]. Some quasistationary mesoscale eddies in the central Japan Basin area, including the eddies studied in this section, are generated in the thermocline and deep Japan Basin water over the mesoscale bottom troughs and sea mounts.

Figure 6.18 demonstrates the monthly mean velocity fields in July and October in the 6th model layer in the deep Japan Basin area (see Fig. 6.17a). The system of ACEs and CEs in the velocity field varies from July to October–November. The most stable one is an ACE simulated in the central region of the studied area over a mesoscale bottom trough. It is a trough between the steepest slope of the Yamato Rise near the southern–southeastern edge of the area and high sea mounts of the Tarasov Rise, the Vasilkovsky Ridge up to 1700 m (42^∘ N, 134^∘ E) and the Bersenev Ridge up to 2200 m (42^∘ N, 133. 71^∘ E) in the northern part [16]. This trough is a small southwestern part of the Japan Basin (see Fig. 6.17). The mid-scale cyclonic circulation is formed during model run over the trough. The mesoscale eddies are supposed to be formed in the central area of the trough (and in the center of the mid-scale cyclonic circulation) due to baroclinic instability of sea currents and bottom topography effects. This quasistationary ACE is situated over the mesoscale bottom saddle between bottom depression in the southern and northern edges of the saddle and between sea mounts in the eastern and western parts. Its center is shifting with time during the model run from July to November in the vicinity of the point with coordinates 41. 15^∘ N and 134^∘ E where similar topographically controlled ACEs have been often observed [47–49]. The studied topographically controlled mesoscale ACE looks like an eddy separated off the current in the cyclonic circulation and stagnating over the complicated bottom topography between sea mounts and bottom depressions. Moreover, it also interacts with surrounding mesoscale CEs.

Fig. 6.18

Simulated velocity field in the studied area in the 6th layer averaged over (a ) July and (b ) October of a typical year

6.3.3 Three-Dimensional Structure and Evolution of Eddies in the Japan Basin

The drift map in Fig. 6.19a clearly demonstrates a vortex pair with two ACEs in the 9th layer with elliptic points at their centers 41^∘ N, 134^∘ E and 41. 4^∘ N, 133. 9^∘ E and a hyperbolic point in between at 41. 3^∘ N, 134^∘ E. The boundary of the northern eddy can be identified as a closed curve with the maximal local gradient of the tracer’s displacement, D, that separates waters involved in the rotational motion around the vortex center from ambient waters. Magnitude of the absolute displacements for the former ones are much smaller than that for the particles outside the eddy.

Fig. 6.19

Manifestation of modeled eddies on July 23 in the ninth layer on (a ) the drift map (D in km) and (b ) the combined forward-in-time (Λ ₊) and backward-in-time (Λ ₋) FTLE maps with the velocity field imposed. Λ is in days⁻¹. “Instantaneous” elliptic and hyperbolic points, to be present in the area on July 23, are indicated by the triangles and crosses, respectively

The FTLE field provides complementary information on the horizontal eddy structure. We computed forward (Λ ₊) and backward-in-time (Λ ₋) FTLE maps by the method described in Sect. 4.3.1 for 30 days in the future and in the past, respectively, starting from July 23. The combined map in Fig. 6.19b demonstrates the same vortex pair as in Fig. 6.19a. The eddy may be identified in the combined FTLE field as a closed region bounded by the black ridges intersecting at two hyperbolic points. Water parcels on one side of the ridge are involved in the vortex motion around the elliptic point, whereas the ones on the other side move downstream away from the eddy. For comparison, we compute the Okubo–Weiss parameter and vorticity field in the same area. It is evident that the eddies can be identified more clearly on the drift and FTLE maps (Fig. 6.19) than in those fields (see Fig. 6.20).

Fig. 6.20

(a ) Manifestations of the simulated eddies on July 23 in the ninth layer in the field of the Okubo–Weiss parameter, Q. Vortex motion (red color) occurs if the vorticity prevails over the deformation, i.e., if W < 0. (b ) The relative vorticity, $\mathop{\mathrm{rot}}\nolimits U$, in the area

The southern eddy has a more complicated structure because of its intensive interaction with ambient waters during the month of integration. The drift maps allow to delineate the transport pathways by which eddies could exchange water with their surroundings. They look like dark “tongues” in Fig. 6.19a encircling that eddy. The origin of those waters can be traced out by computing tracer’s displacements in zonal and meridional directions backward in time for the month, from July 23 to June 23. The corresponding zonal and meridional drift maps shown in Fig. 6.21 allow to visualize where the waters in the ninth layer came from. Blue color of the water tongues around that eddy mean that it captured water from the south (Fig. 6.21a) and east (Fig. 6.21b). Complementary backward-in-time Lagrangian longitudinal (Fig. 6.22a) and latitudinal (Fig. 6.22b) drift maps show by color the longitudes and latitudes, respectively, from which tracers, initialized in the area on June 23, came to their final positions on July 23.

Fig. 6.21

(a ) Backward-in-time meridional drift map shows tracer’s displacements in the area with the simulated eddies in the meridional direction for the month, from July 23 to June 23. The color codes the displacement from the south to north (blue) and vice versa (red). (b ) Backward-in-time zonal drift maps show tracer’s displacements in the zonal direction for the same period. The color codes the displacement from the east to west (blue) and vice versa (red). Both the displacements, Δ λ and Δ ϕ, are computed in the ninth layer of the model in geographic degrees

Fig. 6.22

(a ) Backward-in-time longitudinal drift map in the area with the simulated eddies (the ninth layer) with the color coding the longitudes, λ, from which the tracers, initialized on June 23, came to their final positions on July 23. (b ) Backward-in-time latitudinal drift map with the color coding the latitudes, ϕ, from which the tracers, initialized on June 23, came to their final positions on July 23

The sharp boundary between waters with high gradients of a Lagrangian indicator (e.g., the absolute displacement D) was called a “Lagrangian front” in [25, 29] (see Chap. 8). The Lagrangian fronts, encircling each of the eddies in the pair in Fig. 6.19a, can be identified by a narrow white stripe demarcating the curve with the maximal gradient of D. White color means that the corresponding particles have experienced very small displacements over the period of integration because they rotated around the eddy’s centers. The sizes of the southern and northern simulated eddies are estimated to be ≃ 35 × 45 km and ≃ 20 × 20 km, respectively.

Trajectories of fluid parcels and stationary points in a velocity field can gain and lose hyperbolicity over time. It means, in particular, that hyperbolic stationary points may appear and disappear in the course of time. Only those ones, which exist on July 23, are shown in Fig. 6.19. As to the southern eddy, it is confined from the east and south by the S-like unstable manifold of the hyperbolic point located between the eddies in the vortex pair. Any unstable manifold influences strongly on adjacent fluid parcels. It is illustrated in Fig. 6.23, where we placed blue and rose patches with tracers near the S-like unstable manifold, and advected them forward in time for three and half months. Both the patches elongate along that manifold. The red patch was chosen in the center of the northern eddy and is shown in Fig. 6.23 to deform slightly in the course of time until the northern eddy begins to break down to the end of summer. The southern eddy is confined from the west by the unstable manifold of a hyperbolic point which disappeared to July 23 but existed before. The complicated pattern of the black ridges around the southern eddy in Fig. 6.19b confirms the conclusion about its intensive interaction with ambient waters.

Fig. 6.23

Evolution of 3 patches with tracers in the 9th layer initialized on July 3 in the area with the simulated vortex pair (see Figs. 6.21 and 6.22 above). The red patch was chosen in the center of the northern eddy, the blue and rose ones—on a S-like unstable manifold somewhere at the black ridge encircling the eddies. The blue and rose patches elongated from the beginning along the same unstable manifolds. The red patch deforms slightly in the course of time until the northern eddy begins to break down to the end of summer. After that, it elongates along an unstable manifold of the survived southern eddy

To illustrate the vertical structure of the vortex pair and its evolution we show in Fig. 6.24 the summer FTLE maps in the first, third, fifth, and ninth layers. On July 23 the pair with two ACEs, elliptic points at their centers, and a hyperbolic point in between are clearly seen in the lower layers below the 4th one. The vortex pair is especially prominent in the 9th layer, that is a lower boundary of the main pycnocline. It is not recognizable in the third layer and above. The elliptic points are absent at the surface where there are no signs of vortex motion. In the course of time, the pattern changes. The pair gradually decays in the sense that the northern eddy merges with the southern one (compare the map on August 7 with the map on August 22 when the northern elliptic point disappears in the 9th layer). As to the other layers, it is seen that the northern elliptic point disappears earlier. It is possible to recognize on August 22 a single ACE with the size ≃ 40 × 50 km in the 5th layer and below. We see the ACE that has not reached the surface to the end of summer.

Fig. 6.24

Vertical structure of simulated eddies in summer and its evolution. The FTLE maps in the 1st, 3rd, 5th, and 9th layers are shown on July 23, August 7 and 22 from the top to the bottom, respectively. The vortex pair, seen in the lower layers, evolves gradually with time in a single eddy which, however, is not visible in the surface layers

Changes in the vertical vortex structure in September and October are shown in Fig. 6.25. The eddy in fall is clearly visible in the 5th layer and below as a single ACE of the same size as in August. As to the surface layers, a prominent eddy structure becomes visible there only to the end of October. In the beginning of September, the elliptic point appears in the first layer at the place where the eddy is visible in the 5th layer and below, but the eddy cannot be clearly detectable on the corresponding FTLE maps. Thus, the bowl-shaped eddy is formed to the end of October. It penetrates from the surface to the bottom gradually decaying to the end of November.

Fig. 6.25

The same as in Fig. 6.24 but in fall on September 3, October 10 and 25. The eddy appears at the surface to the end of October

Ten layers have been used in the MHIM adopted to the Japan Sea. In order to illustrate transformation of the studied vortex structure with time, we compute vertical zonal and meridional sections across the simulated eddy. Figures 6.26 and 6.27 show evolution of its vertical structure from late July to late October in terms of sections of quasi-isopycnic layer interfaces (Fig. 6.26) and water temperature in the layers (Fig. 6.27). The studied anticyclonic eddies have been formed over the mesoscale bottom trough in early July, at first, in the main pycnocline and underlying layers and were present within the layers from the 4th one and below all the time after its formation.

Fig. 6.26

Zonal (along 41^∘ N, the upper row) and meridional (along 134^∘ E, the lower row) sections of the interfaces between modeled eddy layers on July 23, September 3, and October 25. Each quasi-isopycnic layer is shown by its own color

Fig. 6.27

The same as in Fig. 6.26 but for temperature sections across the simulated eddy on July 23, September 3, and October 25

The Lagrangian maps on July 23 in Fig. 6.19 clearly show the vortex pair oriented in the meridional direction. The zonal sections in Fig. 6.26 along the latitude 41^∘ N cross the southern ACE which is manifested as a depression of the layers from the 3rd to 9th ones around the elliptic point. The vortex pair evolves to September 3 to a single ACE (see Fig. 6.25) whose zonal cross-section is shown in Fig. 6.26b. It still does not extend to the surface. To October 25 the eddy reaches the surface (see Figs. 6.25 and 6.26c). The northern ACE of the vortex pair, seen in Fig. 6.19 on July 23, is hardly visible in the meridional cross-section as a small depression in the lower layers to the right of the main depression (Fig. 6.26d and e).

From July to early September, the ACE is present only occasionally in the numerical solution in the upper mixed layer (the layer 1) and in the seasonal pycnocline (the layers 2–4). In this period of warm season, when the upper mixed layer is comparatively thin (see Fig. 6.26a, b, d, and e) and the seasonal pycnocline is very strong (see Fig. 6.27a, b, d, and e), the simulated ACE is unstable in the upper layers. Its lifetime in these layers does not exceed a few days. During summer, it episodically appears and breaks down into smaller submesoscale eddies in the upper layers. During October–November, when the thickness of the upper mixed layer increases from 10 to 15–30 m (Fig. 6.26c and f) and the seasonal pycnocline is weak, the ACE becomes as stable in the upper layers as in the underlying ones. It is also manifested in the zonal temperature section in Fig. 6.27c as the closed isotherm at the sea surface.

During the oceanographic CTD-hydrochemical survey in summer 1999 [49], the mesoscale ACE (with the center approximately at the same place as the M3 mooring [47] and our simulated eddy) has been observed in temperature, salinity, dissolved oxygen, and NO₃ sections along 134^∘ E and 41. 25^∘ N. The warm fresh core of the eddy with high gradients in temperature, salinity, and dissolved oxygen at its edge was situated in the thermocline within the layer from 50 to 150 m.

Figure 6.28 shows water temperature structure of that ACE in zonal and meridional sections of the oceanographic survey in early August 1999 [49]. The density gradient in this eddy basically depends on the temperature gradient. The eddy core, surrounded by maximal temperature and density gradients, looks like a lens. The eddy occupies the water column below the seasonal pycnocline (30–50 m). The anticyclonic eddy was not clearly observed in the upper mixed layer and in the seasonal pycnocline both in the zonal and meridional temperature sections. It is an important feature of the observed eddy closely related to the simulation results discussed above. Eddies with similar vertical structure in temperature and density cross-sections, named as intrathermocline eddies, have been observed to the south of the Subarctic Front over the western side of the Yamato Rise and within quasistationary meanders of the Tsushima Current [12]. They have been successfully simulated in this area [13] using an isopycnal ocean circulation model. The observed eddy in Fig. 6.28 is situated over the mesoscale bottom trough surrounded by sea mounts in the western area of the Japan Basin (see Fig. 6.17a and b) practically in the same area as our simulated eddy. In summer, the position and the vertical structure of the simulated ACE in Figs. 6.26 and 6.27 are similar to those for the observed ACE in Fig. 6.28. Both the simulated and observed ACEs have the similar eddy core, the relief of layer interfaces and isotherms.

Fig. 6.28

(a ) Zonal (along 41^∘ N) and (b ) meridional (along 134^∘ E) observed sections of temperature across the ACE to be found during the oceanographic CTD-hydrochemical survey in early August 1999 [49]

The observed ACE is stronger than the simulated one with a much more strong temperature/density front situated to the south of the ACE and a stronger vertical stratification. That difference may be explained by the fact that the observation has been made in the warm climatic period and warm year (1999), whereas the simulation has been performed under daily meteorological conditions averaged over 25-years period from 1976 to 2000. Moreover, we did not take into account meridional heat advection from the southern sea area and the southern boundary of the model domain due to no-slip boundary condition for the current velocity.

To visualize the origin and fate of water masses inside the eddy, a large number of tracers (250,000) were distributed on September 1 in each layer around the eddy center inside the patch 7 × 11 km [133. 87^∘ E–133. 97^∘ E; 41^∘ N–41. 1^∘ N]. They have been advected for 2 months forward and backward in time by the velocity field in each layer. The tracking maps are computed as follows. The area under study [131^∘ E–136^∘ E; 40^∘ N–43. 5^∘ N] is divided into 500 × 500 cells. We compute how many tracers have visited each cell from September 1 to November 1 (forward-in-time tracking maps) and from September 1 to July 1 (backward-in-time tracking maps).

The results are shown in Fig. 6.29 and may be interpreted as follows. The forward-in-time tracking maps in Fig. 6.29a show where the corresponding tracers in each chosen layer were walking from September 1 to November 1. In this period, the tracers from the patches in the lower layers have rotated around the eddy center with an insignificant flow outside in the 5th layer. The “tail” on the upper plane means that at the surface those tracers have been transported by a current to the southeast, i.e., the eddy did not exist at the surface most part of that period.

Fig. 6.29

Tracking maps for the tracers distributed over the eddy’s core on September 1 in the 1st, 5th, 7th, 9th, and 10th layers numbered in the left lower corners. (a ) The forward-in-time map shows where the corresponding tracers were walking from September 1 to November 1. (b ) The backward-in-time map shows where they were walking from September 1 to July 1. The density of traces is in the logarithmic scale

The backward-in-time tracking maps in Fig. 6.29b show that the tracers in the layers from the 7th to 10th have rotated around the eddy center preserving the eddy core in these layers for 2 months in the past. It means that the eddy existed in those layers all that time at the same place without exchanging by the core water with its surroundings. The “tail” in the 5th layer means that the eddy in this layer gained the water from the south, but its core has been at the same place for the 2 months in the past. As to the surface layer, the tracers from the initial patch in the 1st layer came to their positions on September 1 from the west. So the eddy did not exist at the surface in summer. Those conclusions are confirmed by the FTLE maps in Figs. 6.24 and 6.25.

The main ACE under study is an eddy-like feature in the region of the Japan Basin to the north of the Yamato Rise (see Fig. 6.17a). That eddy has been found to be practically stationary for a half-year integration period including summer and fall. It is seen from the lower panels in Figs. 6.24 and 6.25 that displacement of its elliptic point for 3 months did not exceed 10 km. Inspection of the AVISO velocity field at the sea surface for 1992–2014 [AVISO] has shown that surface eddy-like anticyclonic features often appeared in the area around 134^∘ E, 41^∘ N in cold seasons and disappeared in warm ones. No significant directed transport of such eddies has been found in those altimetric data. Taking into account these findings, complicated bottom topography in the area with underwater seamounts and trenches (see Fig. 6.17b) and observations [47, 48], it is reasonable to suppose that we deal with the ACE constrained by bottom topography.

Computations of the FTLEs and particle’s displacements in each depth layer clearly show that the simulated ACE evolves from the eddy that does not reach the surface in summer into a one reaching the surface in fall. The corresponding elliptic points, demarcating the eddy’s center, are absent in the upper layers in summer (Fig. 6.24) and appear in fall (Fig. 6.25). This result is confirmed by computing deformation of the model layers and the temperature cross-sections. Whether the eddy reaches the surface or not depends on the stratification measure in the thermocline, topographic, and other parameters. In summer, when the upper mixed layer is comparatively thin and the stratification of seasonal pycnocline is very strong, the simulated eddy is unstable in the upper layers. In fall, when the stratification of seasonal pycnocline is much weaker than in summer, the eddy becomes as stable in the upper layers as in the underlying ones.

The eddy must be sufficiently nonlinear to exist as a stable entity. The measure of the nonlinearity is the so-called quasigeostrophic nonlinearity parameter Q _β , which is the ratio of the relative vorticity advection to the planetary vorticity advection [7] defined as Q _β  = U∕β L ², where U is the maximum rotational speed, L the eddy radius, and β is the planetary vorticity gradient. To estimate the quasigeostrophic nonlinearity parameter of our simulated eddy in the Japan Basin, we take U = 0. 05–0. 1 m s⁻¹, L = 30, 000 m, and β = 1. 73 ⋅ 10⁻¹¹ m s⁻¹ to get Q _β  = 3. 3–6. 6. This range of values means that the relative vorticity dominates and suggests that our simulated eddy is nonlinear. We may conclude that the quasistationary simulated eddy persists as a stable entity during the simulation period. That conclusion is based not only on the Q _β criterion, but it is also confirmed by different Lagrangian diagnostics including daily FTLE and drift maps (see Figs. 6.19, 6.24, and 6.25) and existence of elliptic points in the eddy’s center in the lower layers during the simulation period (see Figs. 6.19, 6.24, and 6.25).