Tatyana V. Belonenko

A new Lagrangian approach for the three-dimensional analysis of mesoscale eddies, the R-tube method, is presented as an extension of the Lagrangian Eddy Boundary Delineation Algorithm. The method is applied to the quasi-persistent Lofoten anticyclone in the Norwegian Sea using a high-resolution Regional Ocean Modeling System simulation. A horizontal R-contour constructed at 400 m is vertically extrapolated over the 0–1000 m range to form a unified pseudo-three-dimensional eddy boundary. Three-dimensional trajectories of approximately 1 × 106 passive markers are computed over 40 days to investigate material exchange between the vortex and the surrounding flow. The results reveal a strongly coherent subsurface regime extending from 100 to 1000 m and a dynamically distinct surface layer. Within the subsurface vortex, rotational trapping strongly suppresses radial material transport, whereas exchange occurs intermittently through localized finite-time deformation, lobe formation, and lobe detachment. Thus, material export is organized into coherent pulses rather than continuous leakage, indicating that deformation at the vortex periphery provides the principal pathway for releasing water from the isolated core. The eddy core (150–900 m) retains most markers throughout the simulation, demonstrating strong Lagrangian coherence and long-term water-mass isolation. The R-tube method therefore provides a quantitative framework for linking three-dimensional vortex structure, coherent transport, and intermittent material exchange in geophysical flows.

Using the 2002 Kuroshio cyclonic ring as a case study, we document that a cyclonic meander north of the Kuroshio Extension can evolve into a detached ring that crosses the jet and transports water masses across to the southern side of the current, and we use this event as a testbed for comparing different detection methodologies. We combine satellite altimetry with complementary Eulerian and Lagrangian diagnostics to resolve the formation, detachment, and post-detachment evolution of the ring, including its center trajectory, boundary evolution, and transport pathway across the jet. The results show that the ring develops from a cyclonic meander north of the main Kuroshio jet axis, then detaches and is advected to the southern side of the jet while maintaining a coherent core. These results illustrate that ring shedding provides a pathway for cross-jet transport, and highlight how the choice of Eulerian vs Lagrangian diagnostic strongly influences the quantitative characterization of the eddy's size, shape, and lifetime, even when the physical phenomenon itself is robustly identified.

The Kuroshio Extension is one of the most energetic frontal systems in the World Ocean, separating subtropical and subarctic water masses. Mesoscale eddies regularly cross this front, enabling cross-jet transport of heat, salt, and hydrographic properties despite the barrier nature of the jet. Previous studies have mainly focused on the horizontal component of this transport, while the vertical evolution of eddies remains poorly understood. Here, we present a quantitative investigation of mesoscale eddy transformation during Kuroshio Extension crossing using two representative events: a cyclonic ring (2002) and an anticyclonic ring (2024). Three-dimensional eddy structure was examined before, during, and after frontal crossing. Results show that crossing a density front causes not only horizontal transport but also substantial vertical adjustment of eddy cores driven by buoyancy changes relative to surrounding waters. The cyclonic ring, transporting dense subarctic waters into the subtropical region, exhibits a 320 m deepening of the σθ = 26.50 kg m−3 isopycnal, a 400 m deepening of the 5 °C isotherm, and a 200–500 m downward displacement of S = 34.0 Practical Salinity Unit isohaline boundaries. In contrast, the anticyclonic ring undergoes a maximum transient uplift of 150 m of the σθ = 26.50 kg m−3 isopycnal during frontal crossing, followed by partial relaxation to a net uplift of 100 m. Similar behavior is observed for the upper saline-core boundary and the 5 °C isotherm. Simultaneously, the warm saline lens transforms into a dome-shaped structure. This restructuring involves changes in eddy geometry and the distributions of temperature, salinity, and velocity. We propose a buoyancy-controlled mechanism of vertical eddy adjustment after frontal crossing, applicable to mesoscale eddies interacting with major density fronts throughout the World Ocean.

The paper shows that traditional Eulerian approaches, which describe only velocity and concentration fields, but not the actual trajectories of hazardous substances and objects, are fundamentally insufficient for solving the problems of the Russian Ministry of Emergency Situations in the marine environment. Based on Lagrangian modeling, the paper demonstrates the possibilities of operational forecasting of the transport of oil and anthropogenic pollutants, radioactive emissions from accidents at coastal nuclear power plants, as well as the drift of bodies and shipwrecks in the context of complex multiscale ocean circulation. Examples that are directly related to the activities of the Ministry of Emergency Situations (the accident in Chazhma Bay, a hypothetical oil spill in the Kozmino port, pollution in the South-Eastern Baltic, anthropogenic pressure in the Taganrog Bay, and the consequences of accidents at the Kashiwazaki-Kariwa and Fukushima-1 nuclear power plants) are considered, for which Lagrangian analysis allows us to identify transport corridors, areas of pollution accumulation, and temporary “windows” of risk. It is shown that the integration of Lagrangian modeling.

The Taganrog Bay is the most ecologically vulnerable water area of the Sea of Azov, subjected to significant anthropogenic impact from the ports of Mariupol and Taganrog, as well as the Don River discharge. This paper analyzes the processes of potential pollution transfer from the bay into the Sea of Azov using a three-dimensional Princeton Ocean Model hydrodynamic model and Lagrangian modeling of passive particle trajectories. Model circulation was calculated for 2020 with high spatial resolution, followed by numerical tracking of 7,350,000 virtual particles placed in the main pollution zones. Lagrangian analysis identified key transport pathways, accumulation and retention zones for pollutants, and seasonal variability of water exchange through the Dolzhansky Strait. It is shown that the transfer of potential pollution is determined by a combination of wind forcing, Don discharge, and local circulation. Comparison of model results with MODIS satellite data (2000–2024) confirms the spatial patterns of organic matter distribution and the identified transport directions. The obtained results can be used to assess ecological risks associated with the outflow of pollution into the Sea of Azov and to justify environmental protection measures in the region.

This study shows that for weakly unstable Rossby wave regimes, the classical dispersion relation, which relates complex corrections to frequency and wavenumber, has an exception. In the space of wave vectors, there is a point at which the zonal component of the group velocity of Rossby waves becomes zero. This point forms the second branch of the Rossby neutral wave frequency curve, characterized by complex wavenumbers. Thus, the paradigm according to which a complex frequency corresponds to a complex wavenumber has exceptions in the case of Rossby waves.

In connection with the planned prolonged discharge of tritium-containing water from the Fukushima Daiichi Nuclear Power Plant, a gradual increase in tritium concentrations is expected in the coastal waters of the Far Eastern regions of the Russian Federation. The aim of this study is to improve the methods for ensuring the radiation safety of the population under conditions of long-term discharge of radioactive water from the Fukushima Daiichi Nuclear Power Plant based on numerical modeling of ocean current circulation. Materials and Methods : Seawater samples from the coastal areas of Kamchatka, Primorsky, and Khabarovsk Krais, Magadan and Sakhalin Oblasts, and the Chukotka Autonomous Okrug for the period 2023–2025 were used for the analysis of tritium content. Lagrangian models accounting for the spatiotemporal structure of oceanic circulation and currents were employed to describe tritium transport processes. Results and Discussion : The mean values of tritium specific activity in samples collected at distances of up to 1000 m from the shore were shown to range from less than 1.0 Bq/kg to 5.5 Bq/kg. Numerical modeling revealed potential accumulation zones for tritium discharged with treated water from the Fukushima Daiichi Nuclear Power Plant: the Southern Kuril Islands, Sakhalin Island, the southern tip of the Kamchatka Peninsula, and Bering Island. The East Kamchatka Current forms a dynamic barrier along the eastern coast of Kamchatka, limiting the intrusion of contaminated waters into coastal areas. Conclusion : To organize effective long-term monitoring of tritium in seawater and, subsequently, in seafood, it is necessary to refine the areas of the most likely tritium accumulation in the waters of the Russian Far East.

The work is devoted to the quantitative assessment of volume, heat and salt transport through the Near Strait based on GLORYS12V1 data for the period 1993–2021. The paper shows that the predominant direction of water exchange through the strait is inflow from the Pacific Ocean to the Bering Sea. The influence of atmospheric forcing has been established. There is a pronounced seasonal variability in all three parameters, volume, heat, and salt transport, with maximum values recorded in winter and minimum values in summer. The monthly averaged volume transport through the strait varies from 2.8 Sv (1 Sv = 106 m3 · s−1) in September to 4.9 Sv in January, for the heat transport in winter it reaches maximum values of 1.0 × 1018 W, while summer values do not exceed 7.5 × 1017 W. Salt transport shows seasonal variability too: in the cold season, the monthly averaged values are 1.6 × 1015–1.8 × 1015 g · s−1 and in the warm season it does not exceed 1.3 × 1015 g · s−1. The analysis of interannual variability revealed extreme values: in 1995, 2017 and 2018, the maximum average daily volume transport exceeding 15 Sv was recorded, while the minimum values (less than −5 Sv) were observed in 1998, 2000 and 2021. The absolute peaks of salt transport (5.7 × 1015 g · s−1) and volume transport (15.6 Sv) were recorded in 1995, and the peak of heat transport (3.2 × 1018 W) occurred in 2017–2018. On the contrary, 2021 was marked by record low values of all parameters: heat transport reached −1.7 × 1018 W, salt transport −2.7 × 1015 g · s−1, and volume transport −7.6 Sv. The influence of mesoscale eddies on water exchange is described: an inflow in 2018 was formed when the Alaskan jet Stream passes through the strait in the absence of the blocking action of eddies or when the waters leave the periphery of the eddies in a northerly direction, while the negative transport rate (outflow) in 1998 was formed by “blocking” the penetration of the Alaskan Stream by mesoscale eddies with an increase in the North Aleutian slope current in the southeastward direction.

A new study is presented on the transport of markers (virtual particles) at the periphery of a quasi-stationary anticyclonic Lofoten vortex using R-contours calculated with the Lagrangian eddy boundary delineation algorithm (LEBDA) and archiving, validation and interpretation of Satellite Oceanographic data geostrophic velocities. It is shown that LEBDA has advantages over classical Eulerian approaches (e.g., automated mesoscale eddy detection algorithm): it minimizes abrupt changes in the eddy boundaries and reliably identifies the formation and evolution of lobes, which play a key role in the exchange of matter between the eddy and the surrounding flow. The obtained maps of marker escape times from the eddy and the number of rotations demonstrate spatial-azimuthal heterogeneity: some particles are retained for more than 180 days, while others leave the eddy quickly, confirming the existence of a coherent core and “sticky” zones at the boundaries. Verification using a drifter trajectory confirms the real nature of the identified processes of capture, retention, and escape of the markers from the vortex. Analysis of the escape-function and escape-fractal graphs reveals that markers leave the eddy in portions. Each such portion is reflected on the graphs as U-shaped and step-like structures. The partitioned (or intermittent) release of particles, as well as the dependence of the exit time on the initial position, indicates a fractal structure in the escape paths of markers from the vortex and suggests that chaotic advection is the dominant mechanism of water exchange between the eddy and the ambient flow.