891 research outputs found
Route to hyperchaos in Rayleigh-Benard convection
Transition to hyperchaotic regimes in Rayleigh-Benard convection in a square
periodicity cell is studied by three-dimensional numerical simulations. By
fixing the Prandtl number at P=0.3 and varying the Rayleigh number as a control
parameter, a bifurcation diagram is constructed where a route to hyperchaos
involving quasiperiodic regimes with two and three incommensurate frequencies,
multistability, chaotic intermittent attractors and a sequence of boundary and
interior crises is shown. The three largest Lyapunov exponents exhibit a linear
scaling with the Rayleigh number and are positive in the final hyperchaotic
attractor. Thus, a route to weak turbulence is found
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
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
Origin of solar torsional oscillations
Helioseismology has revealed many details of solar differential rotation and
also its time variation, known as torsional oscillations. So far there is no
generally accepted theoretical explanation for torsional oscillations, even
though a close relation to the solar activity cycle is evident. On the
theoretical side non-kinematic dynamo models (including the Lorentz force
feedback on differential rotation) have been used to explain torsional
oscillations. In this paper we use a slightly different approach by forcing
torsional oscillations in a mean field differential rotation model. Our aim is
not a fully self-consistent model but rather to point out a few general
properties of torsional oscillations and their possible origin that are
independent from a particular dynamo model. We find that the poleward
propagating high latitude branch of the torsional oscillations can be explained
as a response of the coupled differential rotation / meridional flow system to
periodic forcing in mid-latitudes, of either mechanical (Lorentz force) or
thermal nature. The speed of the poleward propagation sets constraints on the
value of the turbulent viscosity in the solar convection zone to be less than
3x10^8 m^2/s. We also show that the equatorward propagating low latitude branch
is very unlikely a consequence of mechanical forcing (Lorentz force) alone, but
rather of thermal origin due to the Taylor-Proudman theorem.Comment: 11 pages, 7 figures. accepted by Astrophys.
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
Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow
We present independent observations of the solar-cycle variation of flows
near the solar surface and at a depth of about 60 Mm, in the latitude range
. We show that the time-varying components of the meridional flow
at these two depths have opposite sign, while the time-varying components of
the zonal flow are in phase. This is in agreement with previous results. We
then investigate whether the observations are consistent with a theoretical
model of solar-cycle dependent meridional circulation based on a flux-transport
dynamo combined with a geostrophic flow caused by increased radiative loss in
the active region belt (the only existing quantitative model). We find that the
model and the data are in qualitative agreement, although the amplitude of the
solar-cycle variation of the meridional flow at 60 Mm is underestimated by the
model.Comment: To be published in Solar Physcis Topical Issue "Helioseismology,
Asteroseismology, and MHD Connections
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
Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: Saturation mechanism and torsional oscillations
In this paper we discuss a dynamic flux-transport dynamo model that includes
the feedback of the induced magnetic field on differential rotation and
meridional flow. We consider two different approaches for the feedback:
meanfield Lorentz force and quenching of transport coefficients such as
turbulent viscosity and heat conductivity. We find that even strong feedback on
the meridional flow does not change the character of the flux-transport dynamo
significantly; however it leads to a significant reduction of differential
rotation. To a large degree independent from the dynamo parameters, the
saturation takes place when the toroidal field at the base of the convection
zone reaches between 1.2 an 1.5 T, the energy converted intomagnetic energy
corresponds to about 0.1 to 0.2% of the solar luminosity. The torsional
oscillations produced through Lorentz force feedback on differential rotation
show a dominant poleward propagating branch with the correct phase relation to
the magnetic cycle. We show that incorporating enhanced surface cooling of the
active region belt (as proposed by Spruit) leads to an equatorward propagating
branch in good agreement with observations.Comment: 15 pages, 12 figures, Accepted for publication in ApJ August 10
issue; corrected typos, corrected referenc
On the Fredholm property of bisingular pseudodifferential operators
For operators belonging either to a class of global bisingular
pseudodifferential operators on or to a class of bisingular
pseudodifferential operators on a product of two closed smooth
manifolds, we show the equivalence of their ellipticity (defined by the
invertibility of certain associated homogeneous principal symbols) and their
Fredholm mapping property in associated scales of Sobolev spaces. We also prove
the spectral invariance of these operator classes and then extend these results
to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added
reference
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
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