arXiv subjects

M. Yu. Uleysky

Publications and source records attributed to M. Yu. Uleysky.

32 records · Page 2Linked to original sources

arXiv2012

Lagrangian study of transport and mixing in a mesoscale eddy street

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 are 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 eddy's center.

physics.ao-ph↗

arXiv2012

Mechanism of destruction of transport barriers in geophysical jets with Rossby waves

The mechanism of destruction of a central transport barrier in a dynamical model of a geophysical zonal jet current in the ocean or the atmosphere with two propagating Rossby waves is studied. We develop a method for computing a central invariant curve which is an indicator of existence of the barrier. Breakdown of this curve under a variation of the Rossby wave amplitudes and onset of chaotic cross-jet transport happen due to specific resonances producing stochastic layers in the central jet. The main result is that there are resonances breaking the transport barrier at unexpectedly small values of the amplitudes that may have serious impact on mixing and transport in the ocean and the atmosphere. The effect can be found in laboratory experiments with azimuthal jets and Rossby waves in rotating tanks under specific values of the wave numbers that are predicted in the theory.

nlin.CD↗

arXiv2011

Effect of dynamical traps on chaotic transport in a meandering jet flow

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 dynamical, 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 the vortex cores) filled with the particles moving in the same frame and the saddle traps connected with periodic saddle trajectories. 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.

nlin.CD↗

arXiv2010

Level spacing statistics in a randomly-inhomogeneous acoustic waveguide

Dynamics of a randomly-perturbed quantum system with 3/2-degrees of freedom is considered. We introduce a transfer operator being the quantum analogue of the specific Poincaré map. This map was proposed in (Makarov, Uleysky, J. Phys. A: Math. Gen., 2006) for exploring domains of finite-time stability, which survive under random excitation. Our attention is concentrated on level spacing distribution of the transfer operator, averaged over ensemble of realizations. The problem of sound propagation in an oceanic waveguide is considered as an example. For the acoustic frequency of 200 Hz, level spacing distribution undergoes the crossover from Poissonian to Wigner-like statistics with increasing time, as it is consistent with classical predictions via the specific Poincaré map. For the frequency of 600 Hz, the level spacing statistics becomes non-universal due to large number of nearly-degenerate levels whose contribution grows with time. Occurrence of nearly-degenerate levels is attributed to bifurcations of classical periodic orbits, caused by fast spatial oscillations of the random perturbation.

nlin.CD↗

arXiv2009

Detecting barrier to cross-jet Lagrangian transport and its destruction in a meandering flow

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 phase 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.

nlin.CD↗

arXiv2007

Unstable periodic orbits in a chaotic meandering jet flow

We study the origin and bifurcations of typical classes of unstable periodic orbits in a jet flow that was introduced before as a kinematic model of chaotic advection, transport and mixing of passive scalars in meandering oceanic and atmospheric currents. A method to detect and locate the unstable periodic orbits and classify them by the origin and bifurcations is developed. We consider in detail period-1 and period-4 orbits playing an important role in chaotic advection. We introduce five classes of period-4 orbits: western and eastern ballistic ones, whose origin is associated with ballistic resonances of the fourth order, rotational ones, associated with rotational resonances of the second and fourth orders, and rotational-ballistic ones associated with a rotational-ballistic resonance. It is a new kind of nonlinear resonances that may occur in chaotic flow with jets and/or circulation cells. Varying the perturbation amplitude, we track out the origin and bifurcations of the orbits for each class.

nlin.CD↗

arXiv2007

Giant acceleration in slow-fast space-periodic Hamiltonian systems

Motion of an ensemble of particles in a space-periodic potential well with a weak wave-like perturbation imposed is considered. We found that slow oscillations of wavenumber of the perturbation lead to occurrence of directed particle current. This current is amplifying with time due to giant acceleration of some particles. It is shown that giant acceleration is linked with the existence of resonant channels in phase space.

nlin.CD↗

arXiv2006

Chaotic mixing and transport in a meandering jet flow

Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model streamfunction, Hamiltonian advection equations, stationary points, and bifurcations. The phase portrait of the chosen model flow in the moving reference frame consists of a central eastward jet, chains of northern and southern circulations, and peripheral westward currents. Under a periodic perturbation of the meander's amplitude, the topology of the phase space is complicated by the presence of chaotic layers and chains of oscillatory and ballistic islands with sticky boundaries immersed into a stochastic sea. Typical chaotic trajectories of advected particles are shown to demonstrate a complicated behavior with long flights in both the directions of motion intermittent with trapping in the circulation cells being stuck to the boundaries of vortex cores and resonant islands. Transport is asymmetric in the sense that mixing between the circulations and the peripheral currents is, in general, different from mixing between the circulations and the jet. The transport properties are characterized by probability distribution functions (PDFs) of durations and lengths of flights. Both the PDFs exhibit at their tails power-law decay with different values of exponents.

nlin.CD↗

arXiv2005

Entanglement, fidelity, and quantum-classical correlations with an atom walking in a quantized cavity field

Stability and instability of quantum evolution are studied in the interaction between a two-level atom with photon recoil and a quantized field mode in an ideal cavity, the basic model of cavity quantum electrodynamics (QED). It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic walking of the atomic center-of-mass in the quantized field of a standing wave in the absence of any kind of interaction with environment. This kind of quantum instability manifests itself in strong variations of reduced quantum purity and entropy, correlating with the respective classical Lyapunov exponent, and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. The connection between quantum entanglement and fidelity and the center-of-mass motion is clarified analytically and numerically for a few regimes of that motion. The results are illustrated with two specific initial field states: the Fock and coherent ones. Numerical experiments demonstrate various manifestations of the quantum-classical correspondence, including dynamical chaos and fractals, which can be, in principle, observed in real experiments with atoms and photons in high finesse cavities.

quant-ph↗

arXiv2005

Sensitivity of ray dynamics in an underwater sound channel to vertical scale of longitudinal sound-speed variations

We investigate sound ray propagation in a range-dependent underwater acoustic waveguide. Our attention is focused on sensitivity of ray dynamics to the vertical structure of a sound-speed perturbation induced by ocean internal waves. Two models of longitudinal sound-speed variations are considered: a periodic inhomogeneity and a stochastic one. It is found that vertical oscillations of a sound-speed perturbation can affect rays in a resonant manner. Such resonances give rise to chaos in certain regions of phase space. It is shown that stability of steep rays, being observed in experiments, is connected with suppression of resonances in the case of small-scale vertical sound-speed oscillations.

physics.ao-ph↗

arXiv2005

Nonlinear Hamiltonian dynamics of Lagrangian transport and mixing in the ocean

Methods of dynamical system's theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent structures in a randomly fluctuating ocean -- a jet-like current and an eddy. Advection of passive tracers in a periodically-driven flow consisting of a background stream and an eddy (the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere) is analyzed as an example of chaotic particle's scattering and transport. A numerical analysis reveals a nonattracting chaotic invariant set $Λ$ that determines scattering and trapping of particles from the incoming flow. It is shown that both the trapping time for particles in the mixing region and the number of times their trajectories wind around the vortex have hierarchical fractal structure as functions of the initial particle's coordinates. Scattering functions are singular on a Cantor set of initial conditions, and this property should manifest itself by strong fluctuations of quantities measured in experiments. The Lagrangian structures in our numerical experiments are shown to be similar to those found in a recent laboratory dye experiment at Woods Hole. Transport and mixing of passive particles is studied in the kinematic model inspired by the interaction of a jet current (like the Gulf Stream or the Kuroshio) with an eddy in a noisy environment. We demonstrate a non-trivial phenomenon of noise-induced clustering of passive particles and propose a method to find such clusters in numerical experiments. These clusters are patches of advected particles which can move together in a random velocity field for comparatively long time.

nlin.CD↗

arXiv2005

Noise-induced clustering in Hamiltonian systems

The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincaré map, is proposed and justified. Physical manifestations of these regions of stability, the so-called coherent clusters, are demonstrated with two models in ocean physics. We find bunches of sound rays propagating coherently in an underwater waveguide through a randomly fluctuating ocean at long distances. We find clusters of passive particles to be advected coherently by a random two-dimensional flow modelling mixing around a topographic eddy in the ocean.

nlin.CD↗

arXiv2005

On the quantum (in)stability in cavity QED

The stability and instability of quantum motion is studied in the context of cavity quantum electrodynamics (QED). It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic walking of an atom in the quantized field of a standing wave in the absence of any other interaction with environment. This quantum instability manifests itself in strong variations of quantum purity and entropy and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. It is quantified in terms of the respective classical maximal Lyapunov exponent that can be estimated in appropriate in-out experiments.

quant-ph↗

arXiv2003

Ray chaos and ray clustering in an ocean waveguide

We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a random-like sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincaré maps, plots of variations of the action per a ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a random-like multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves.

nlin.CD↗