42 research outputs found
Edge of Chaos and Genesis of Turbulence
The edge of chaos is analyzed in a spatially extended system, modeled by the
regularized long-wave equation, prior to the transition to permanent
spatiotemporal chaos. In the presence of coexisting attractors, a chaotic
saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As
a control parameter is varied, the chaotic transient evolves to well-developed
transient turbulence via a cascade of fractal-fractal metamorphoses. The edge
state responsible for the edge of chaos and the genesis of turbulence is an
unstable travelling wave in the laboratory frame, corresponding to a saddle
point lying at the basin boundary in the Fourier space
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
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
Transition to chaos in a reduced-order model of a shear layer
The present work studies the non-linear dynamics of a shear layer, driven by
a body force and confined between parallel walls, a simplified setting to study
transitional and turbulent shear layers. It was introduced by Nogueira \&
Cavalieri (J. Fluid Mech. 907, A32, 2021), and is here studied using a
reduced-order model based on a Galerkin projection of the Navier-Stokes system.
By considering a confined shear layer with free-slip boundary conditions on the
walls, periodic boundary conditions in streamwise and spanwise directions may
be used, simplifying the system and enabling the use of methods of dynamical
systems theory. A basis of eight modes is used in the Galerkin projection,
representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and
oblique waves, structures observed in the cited work, and also present in shear
layers and jets. A dynamical system is obtained, and its transition to chaos is
studied. Increasing Reynolds number leads to pitchfork and Hopf
bifurcations, and the latter leads to a limit cycle with amplitude modulation
of vortices, as in the DNS by Nogueira \& Cavalieri. Further increase of
leads to the appearance of a chaotic saddle, followed by the emergence of
quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging
crisis for higher , leading to chaotic dynamics with amplitude modulation
and phase jumps of vortices. This is reminiscent of observations of coherent
structures in turbulent jets, suggesting that the model represents dynamics
consistent with features of shear layers and jets.Comment: 28 pages, 18 figure
Transition to chaos and magnetic field generation in rotating Rayleigh-B\'enard convection
Hydrodynamic and magnetohydrodynamic convective attractors in
three-dimensional rotating Rayleigh-B\'enard convection are studied numerically
by varying the Taylor and Rayleigh numbers as control parameters. First, an
analysis of hydrodynamic attractors and their bifurcations is conducted, where
routes to chaos via quasiperiodicity are identified. Second, the behaviour of
the magnetohydrodynamic system is investigated by introducing a seed magnetic
field and measuring its growth or decay as a function of the Taylor number,
while keeping the Rayleigh number fixed. Analysis of the attractors shows that
rotation has a significant impact on magnetic field generation in
Rayleigh-B\'enard convection, with the critical magnetic Prandtl number
changing nonmonotonically with the rotation rate. It is argued that a
nonhysteretic blowout bifurcation with on-off intermittency is responsible for
the transitions to dynamo
A novel type of intermittency in a nonlinear dynamo in a compressible flow
The transition to intermittent mean--field dynamos is studied using numerical
simulations of isotropic magnetohydrodynamic turbulence driven by a helical
flow. The low-Prandtl number regime is investigated by keeping the kinematic
viscosity fixed while the magnetic diffusivity is varied. Just below the
critical parameter value for the onset of dynamo action, a transient
mean--field with low magnetic energy is observed. After the transition to a
sustained dynamo, the system is shown to evolve through different types of
intermittency until a large--scale coherent field with small--scale turbulent
fluctuations is formed. Prior to this coherent field stage, a new type of
intermittency is detected, where the magnetic field randomly alternates between
phases of coherent and incoherent large--scale spatial structures. The
relevance of these findings to the understanding of the physics of mean--field
dynamo and the physical mechanisms behind intermittent behavior observed in
stellar magnetic field variability are discussed.Comment: 19 pages, 13 figure
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
Lagrangian chaos in an ABC--forced nonlinear dynamo
The Lagrangian properties of the velocity field in a magnetized fluid are
studied using three-dimensional simulations of a helical magnetohydrodynamic
dynamo. We compute the attracting and repelling Lagrangian coherent structures,
which are dynamic lines and surfaces in the velocity field that delineate
particle transport in flows with chaotic streamlines and act as transport
barriers. Two dynamo regimes are explored, one with a robust coherent mean
magnetic field and one with intermittent bursts of magnetic energy. The
Lagrangian coherent structures and the statistics of finite--time Lyapunov
exponents indicate that the stirring/mixing properties of the velocity field
decay as a linear function of the magnetic energy. The relevance of this study
for the solar dynamo problem is discussed