On-off intermittency and amplitude-phase synchronization in Keplerian shear flows

We study the development of coherent structures in local simulations of the magnetorotational instability in accretion discs in regimes of on-off intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102 (2010)], we have shown that the laminar and bursty states due to the on-off spatiotemporal intermittency in a one-dimensional model of nonlinear waves correspond, respectively, to nonattracting coherent structures with higher and lower degrees of amplitude-phase synchronization. In this paper we extend these results to a three-dimensional model of magnetized Keplerian shear flows. Keeping the kinetic Reynolds number and the magnetic Prandtl number fixed, we investigate two different intermittent regimes by varying the plasma beta parameter. The first regime is characterized by turbulent patterns interrupted by the recurrent emergence of a large-scale coherent structure known as two-channel flow, where the state of the system can be described by a single Fourier mode. The second regime is dominated by the turbulence with sporadic emergence of coherent structures with shapes that are reminiscent of a perturbed channel flow. By computing the Fourier power and phase spectral entropies in three-dimensions, we show that the large-scale coherent structures are characterized by a high degree of amplitude-phase synchronization.Comment: 17 pages, 10 figure

Nonlinear dynamics of turbulent waves in fluids and plasmas

International audienceIn a model drift wave system that is interesting both in fluids and plasmas, we find that an embedded moving saddle point plays an important role at the onset of turbulence. Here the saddle point is actually a saddle steady wave, in its moving frame the wave system can be transformed into a set of coupled oscillators whose motion is affected by the saddle steady wave as if it is a potential. It is found that a collision with the saddle point triggers a crisis, following the collision another dynamic event occurs which involves a transition in the phase state of the master oscillator. Only after the latter event the spatial regularity is destroyed. The phase dynamics before and after the transition is further investigated. It is found that in a spatially coherent state before the transition the oscillators reach a functional phase synchronization collectively with or without phase slips, after the transition in the turbulent state an on-off imperfect synchronization is established among the oscillators with long wavelengths. When the synchronization is on, their amplitudes grow up simultaneously, giving rise to a burst in the total wave energy. A power law behavior is observed in the correlation function between phases of the oscillators. Potential application of our results in prediction of energy bursts in turbulence is discussed

Existence, uniqueness and analyticity of space-periodic solutions to the regularised long-wave equation

We consider space-periodic evolutionary and travelling-wave solutions to the regularised long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial conditions, and global in time spatial analyticity of such solutions for analytical initial conditions. The width of the analyticity strip decays at most polynomially. We prove existence of travelling-wave solutions and uniqueness of travelling waves of a sufficiently small norm. The importance of damping is demonstrated by showing that the problem of finding travelling-wave solutions to the undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.Comment: 29 pp., 4 figures, 44 reference

Self-modulation of nonlinear Alfven waves in a strongly magnetized relativistic electron-positron plasma

We study the self-modulation of a circularly polarized Alfven wave in a strongly magnetized relativistic electron-positron plasma with finite temperature. This nonlinear wave corresponds to an exact solution of the equations, with a dispersion relation that has two branches. For a large magnetic field, the Alfven branch has two different zones, which we call the normal dispersion zone (where d omega/dk > 0) and the anomalous dispersion zone (where d omega/dk < 0). A nonlinear Schrodinger equation is derived in the normal dispersion zone of the Alfven wave, where the wave envelope can evolve as a periodic wave train or as a solitary wave, depending on the initial condition. The maximum growth rate of the modulational instability decreases as the temperature is increased. We also study the Alfven wave propagation in the anomalous dispersion zone, where a nonlinear wave equation is obtained. However, in this zone the wave envelope can evolve only as a periodic wave train.CONICyT 21100839 74110049FONDECyT 1110135 1110729 1080658 1121144CNPqEuropean Commission for a Marie Curie International Incoming FellowshipInstitute for Fusion Studie

Self-modulation of nonlinear waves in a weakly magnetized relativistic electron-positron plasma with temperature

We develop a nonlinear theory for self-modulation of a circularly polarized electromagnetic wave in a relativistic hot weakly magnetized electron-positron plasma. The case of parallel propagation along an ambient magnetic field is considered. A nonlinear Schrodinger equation is derived for the complex wave amplitude of a self-modulated wave packet. We show that the maximum growth rate of the modulational instability decreases as the temperature of the pair plasma increases. Depending on the initial conditions, the unstable wave envelope can evolve nonlinearly to either periodic wave trains or solitary waves. This theory has application to high-energy astrophysics and high-power laser physics.CONICyTFONDECyT 1110135 1080658Brazilian agency CNPqBrazilian agency FAPESPMarie Curie International Incoming Fellowshiphospitality of Paris ObservatoryInstitute for Fusion Studie

Intermittent chaos driven by nonlinear Alfvén waves

International audienceWe investigate the relevance of chaotic saddles and unstable periodic orbits at the onset of intermittent chaos in the phase dynamics of nonlinear Alfvén waves by using the Kuramoto-Sivashinsky (KS) equation as a model for phase dynamics. We focus on the role of nonattracting chaotic solutions of the KS equation, known as chaotic saddles, in the transition from weak chaos to strong chaos via an interior crisis and show how two of these unstable chaotic saddles can interact to produce the plasma intermittency observed in the strongly chaotic regimes. The dynamical systems approach discussed in this work can lead to a better understanding of the mechanisms responsible for the phenomena of intermittency in space plasmas

Chaotic saddles in nonlinear modulational interactions in a plasma

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres

Nonintegrable Interaction of Ion-Acoustic and Electromagnetic Waves in a Plasma

In this paper we re-examine the one-dimensional interaction of electromagnetic and ion acoustic waves in a plasma. Our model is similar to one solved by Rao et al. (Phys. Fluids, vol. 26, 2488 (1983)) under a number of analytical approximations. Here we perform a numerical investigation to examine the stability of the model. We find that for slightly over dense plasmas, the propagation of stable solitary modes can occur in an adiabatic regime where the ion acoustic electric field potential is enslaved to the electromagnetic field of a laser. But if the laser intensity or plasma density increases or the laser frequency decreases, the adiabatic regime loses stability via a transition to chaos. New asymptotic states are attained when the adiabatic regime no longer exists. In these new states, the plasma becomes rarefied, and the laser field tends to behave like a vacuum field.Comment: 19 pages, REVTeX, 6 ps figures, accepted for publication in Phys. Rev.

Chaos in magnetospheric radio emissions

A three-wave model of auroral radio emissions near the electron plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can occur in the nonlinear evolution of this three-wave process in the magnetosphere. In particular, two types of intermittency, due to either local or global bifurcations, can be observed. We analyze the type-I Pomeau-Manneville intermittency, arising from a saddle-node bifurcation, and the crisis-induced intermittency, arising from an interior crisis associated with a global bifurcation. Examples of time series, power spectrum, phase-space trajectory for both types of intermittency are presented through computer simulations. The degree of chaoticity of this three-wave process is characterized by calculating the maximum Lyapunov exponent. We suggest that the intermit-tent phenomena discussed in this paper may be observed in the temporal signal of magnetospheric radio emissions

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

International audienceThe chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed