One of the most prominent feature of research in Russia and the former Soviet Union is so-called scientific schools. It is a collaboration of researchers with a common scientific background working, as a rule, together in a specific city or even at a
n institution. The genealogical tree of scientific schools on nonlinear dynamics in Russia and the former Soviet Union is grown. We use these terminology in a broad sense including theory of dynamical systems and chaos and its applications in nonlinear physics. In most cases we connect two persons if one was an advisor of the Doctoral thesis of another one. It is an analogue of the Candidate of Science thesis in Russia. If the person had no official advisor or we dont know exactly who was an advisor, we fix that person who was known to be an informal teacher and has influenced on him/her very much.
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic a
dvection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.
Using Lagrangian methods we analyze a 20-year-long estimate of water flux through the Kamchatka Strait in the northern North Pacific based on AVISO velocity field. It sheds new light on the flux pattern and its variability on annual and monthly time
scales. Strong seasonality in surface outflow through the strait could be explained by temporal changes in the wind stress over the northern and western Bering Sea slopes. Interannual changes in a surface outflow through the Kamchatka Strait correlate significantly with the Near Strait inflow and Bering Strait outflow. Enhanced westward surface flow of the Alaskan Stream across the $174^circ$ E section in the northern North Pacific is accompanied by an increased inflow into the Bering Sea through the Near Strait. In summer, the surface flow pattern in the Kamchatka Strait is determined by passage of anticyclonic and cyclonic mesoscale eddies. The wind stress over the Bering basin in winter - spring is responsible for eddy generation in the region.
We present the results of in-situ measurements of $^{134}$Cs and $^{137}$Cs released from the Fukushima Nuclear Power Plant (FNPP) collected at surface and different depths in the western North Pacific in June and July 2012. It was found that 15 mont
h after the incident concentrations of radiocesium in the Japan and Okhotsk seas were at background or slightly increased level, while they had increased values in the subarctic front area east of Japan. The highest concentrations of $^{134}$Cs and $^{137}$Cs up to 13.5 ${pm}$ 0.9 and 22.7 ${pm}$ 1.5 Bq m$^{-3}$ have been found to exceed ten times the background levels before the accident. Maximal content of radiocesium was observed within subsurface and intermediate water layers inside the cores of anticyclonic eddies (100 - 500 m). Even slightly increased content of radiocesium was found at some eddies at depth of 1000 m. It is expected that convergence and subduction of surface water inside eddies are main mechanisms of downward transport of radionuclides. In situ observations are compared with the results of simulated advection of these radioisotopes by the AVISO altimetric velocity field. Different Lagrangian diagnostics are used to reconstruct the history and origin of synthetic tracers imitating measured seawater samples collected in each of those eddies. The results of observations are consistent with the simulated results. It is shown that the tracers, simulating water samples with increased radioactivity to be measured in the cruise, really visited the areas with presumably high level of contamination. Fast water advection between anticyclonic eddies and convergence of surface water inside eddies make them responsible for spreading, accumulation and downward transport of cesium rich water to the intermediate depth in the frontal zone.
The output from an eddy-resolved multi-layered circulation model is used to analyze the vertical structure of simulated deep-sea eddies in the Japan Basin of the Japan/East Sea constrained by bottom topography. We focus on Lagrangian analysis of anti
cyclonic eddies, generated in the model in a typical year approximately at the place of the mooring and the hydrographic sections, where such eddies have been regularly observed in different years (1993--1997, 1999--2001). Using a quasi-3D computation of the finite-time Lyapunov exponents and displacements for a large number of synthetic tracers in each depth layer, we demonstrate how the simulated feature evolves of the eddy, that does not reach the surface in summer, into a one reaching the surface in fall. This finding is confirmed by computing deformation of the model layers across the simulated eddy in zonal and meridional directions and in the corresponding temperature cross sections. Computed Lagrangian tracking maps allow to trace the origin and fate of water masses in different layers of the eddy. The results of simulation are compared with observed temperature zonal and meridional cross sections of a real anticyclonic eddy to be studied at that place during the oceanographic Conductivity, Temperature, and Depth (CTD) hydrochemical survey in summer 1999. Both the simulated and observed eddies are shown to have the similar eddy core and the relief of layer interfaces and isotherms.
Lagrangian approach is applied to study near-surface large-scale transport in the Kuroshio Extension area using a simulation with synthetic particles advected by AVISO altimetric velocity field. A material line technique is applied to find the origin
of water masses in cold-core cyclonic rings pinched off from the jet in summer 2011. Tracking and Lagrangian maps provide the evidence of cross-jet transport. Fukushima derived caesium isotopes are used as Lagrangian tracers to study transport and mixing in the area a few months after the March of 2011 tsunami that caused a heavy damage of the Fukushima nuclear power plant (FNPP). Tracking maps are computed to trace the origin of water parcels with measured levels of Cs-134 and Cs-137 concentrations collected in two R/V cruises in June and July 2011 in the large area of the Northwest Pacific. It is shown that Lagrangian simulation is useful to finding the surface areas that are potentially dangerous due to the risk of radioactive contamination. The results of simulation are supported by tracks of the surface drifters which were deployed in the area.
Sea surface height anomalies observed by satellites in 1993--2012 are combined with simulation and observations by surface drifters and Argo floats to study water flow pattern in the Near Strait (NS) connected the Pacific Ocean with the Bering Sea. D
aily Lagrangian latitudinal maps, computed with the AVISO surface velocity field, and calculation of the transport across the strait show that the flow through the NS is highly variable and controlled by mesoscale and submesoscale eddies in the area. On the seasonal scale, the flux through the western part of the NR is negatively correlated with the flux through its eastern part ($r=-0.93$). On the interannual time scale, a significant positive correlation ($r=0.72$) is diagnosed between the NS transport and the wind stress in winter. Increased southward component of the wind stress decreases the northward water transport through the strait. Positive wind stress curl over the strait area in winter--spring generates the cyclonic circulation and thereby enhances the southward flow in the western part ($r=-0.68$) and northward flow in the eastern part ($r=0.61$) of the NR. In fall, the water transport in different parts of the NS is determined by the strength of the anticyclonic mesoscale eddy located in the Alaskan Stream area.
We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian trajectories a
re computed for a large number of particles in an interpolated velocity field generated by a numerical regional multi-layer eddy-resolving circulation model. We compute finite-time Lyapunov exponents for a comparatively long period of time by the method developed and plot the Lyapunov synoptic map quantifying surface transport and mixing in that region. This map uncovers the striking flow structures along the coast with a mesoscale eddy street and repelling material lines. We propose new Lagrangian diagnostic tools --- the time of exit of particles off a selected box, the number of changes of the sign of zonal and meridional velocities --- to study transport and mixing by a pair of strongly interacting eddies often visible at sea-surface temperature satellite images in that region. We develop a technique to track evolution of clusters of particles, streaklines and material lines. The Lagrangian tools used allow us to reveal mesoscale eddies and their structure, to track different phases of the coastal flow, to find inhomogeneous character of transport and mixing on mesoscales and submesoscales and to quantify mixing by the values of exit times and the number of times particles wind around the eddys center.
We continue our study of chaotic mixing and transport of passive particles in a simple model of a meandering jet flow [Prants, et al, Chaos {bf 16}, 033117 (2006)]. In the present paper we study and explain phenomenologically a connection between dyn
amical, topological, and statistical properties of chaotic mixing and transport in the model flow in terms of dynamical traps, singular zones in the phase space where particles may spend arbitrary long but finite time [Zaslavsky, Phys. D {bf 168--169}, 292 (2002)]. The transport of passive particles is described in terms of lengths and durations of zonal flights which are events between two successive changes of sign of zonal velocity. Some peculiarities of the respective probability density functions for short flights are proven to be caused by the so-called rotational-islands traps connected with the boundaries of resonant islands (including those of the vortex cores) filled with the particles moving in the same frame. Whereas, the statistics of long flights can be explained by the influence of the so-called ballistic-islands traps filled with the particles moving from a frame to frame.
Cross-jet transport of passive scalars in a kinematic model of the meandering laminar two-dimensional incompressible flow which is known to produce chaotic mixing is studied. We develop a method for detecting barriers to cross-jet transport in the ph
ase space which is a physical space for our model. Using tools from theory of nontwist maps, we construct a central invariant curve and compute its characteristics that may serve good indicators of the existence of a central transport barrier, its strength, and topology. Computing fractal dimension, length, and winding number of that curve in the parameter space, we study in detail change of its geometry and its destruction that are caused by local bifurcations and a global bifurcation known as reconnection of separatrices of resonances. Scenarios of reconnection are different for odd and even resonances. The central invariant curves with rational and irrational (noble) values of winding numbers are arranged into hierarchical series which are described in terms of continued fractions. Destruction of central transport barrier is illustrated for two ways in the parameter space: when moving along resonant bifurcation curves with rational values of the winding number and along curves with noble (irrational) values.
