2,194 research outputs found
Is nonhelical hydromagnetic turbulence peaked at small scales?
Nonhelical hydromagnetic turbulence without an imposed magnetic field is
considered in the case where the magnetic Prandtl number is unity. The magnetic
field is entirely due to dynamo action. The magnetic energy spectrum peaks at a
wavenumber of about 5 times the minimum wavenumber in the domain, and not at
the resistive scale, as has previously been argued. Throughout the inertial
range the spectral magnetic energy exceeds the kinetic energy by a factor of
about 2.5, and both spectra are approximately parallel. At first glance, the
total energy spectrum seems to be close to k^{-3/2}, but there is a strong
bottleneck effect and it is suggested that the asymptotic spectrum is k^{-5/3}.
This is supported by the value of the second order structure function exponent
that is found to be \zeta_2=0.70, suggesting a k^{-1.70} spectrum.Comment: 6 pages, 6 figure
Self-similar turbulent dynamo
The amplification of magnetic fields in a highly conducting fluid is studied
numerically. During growth, the magnetic field is spatially intermittent: it
does not uniformly fill the volume, but is concentrated in long thin folded
structures. Contrary to a commonly held view, intermittency of the folded field
does not increase indefinitely throughout the growth stage if diffusion is
present. Instead, as we show, the probability-density function (PDF) of the
field strength becomes self-similar. The normalized moments increase with
magnetic Prandtl number in a powerlike fashion. We argue that the
self-similarity is to be expected with a finite flow scale and system size. In
the nonlinear saturated state, intermittency is reduced and the PDF is
exponential. Parallels are noted with self-similar behavior recently observed
for passive-scalar mixing and for map dynamos.Comment: revtex, 4 pages, 5 figures; minor changes to match published versio
Nonlinear magneto-optical resonances at D1 excitation of 85Rb and 87Rb in an extremely thin cell
Nonlinear magneto-optical resonances have been measured in an extremely thin
cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural
isotopic composition. All hyperfine transitions of both isotopes have been
studied for a wide range of laser power densities, laser detunings, and ETC
wall separations. Dark resonances in the laser induced fluorescence (LIF) were
observed as expected when the ground state total angular momentum F_g was
greater than or equal to the excited state total angular momentum F_e. Unlike
the case of ordinary cells, the width and contrast of dark resonances formed in
the ETC dramatically depended on the detuning of the laser from the exact
atomic transition. A theoretical model based on the optical Bloch equations was
applied to calculate the shapes of the resonance curves. The model averaged
over the contributions from different atomic velocity groups, considered all
neighboring hyperfine transitions, took into account the splitting and mixing
of magnetic sublevels in an external magnetic field, and included a detailed
treatment of the coherence properties of the laser radiation. Such a
theoretical approach had successfully described nonlinear magneto-optical
resonances in ordinary vapor cells. Although the values of certain model
parameters in the ETC differed significantly from the case of ordinary cells,
the same physical processes were used to model both cases. However, to describe
the resonances in the ETC, key parameters such as the transit relaxation rate
and Doppler width had to be modified in accordance with the ETC's unique
features. Agreement between the measured and calculated resonance curves was
satisfactory for the ETC, though not as good as in the case of ordinary cells.Comment: v2: substantial changes and expanded theoretical model; 13 pages, 10
figures; accepted for publication in Physical Review
Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
The small-scale dynamo is a process by which turbulent kinetic energy is
converted into magnetic energy, and thus is expected to depend crucially on the
nature of turbulence. In this work, we present a model for the small-scale
dynamo that takes into account the slope of the turbulent velocity spectrum
v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and
the typical velocity on that scale. The time evolution of the fluctuation
component of the magnetic field, i.e., the small-scale field, is described by
the Kazantsev equation. We solve this linear differential equation for its
eigenvalues with the quantum-mechanical WKB-approximation. The validity of this
method is estimated as a function of the magnetic Prandtl number Pm. We
calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit,
using our model of the turbulent velocity correlation function. For Kolmogorov
turbulence (theta=1/3), we find that the critical magnetic Reynolds number is
approximately 110 and for Burgers turbulence (theta=1/2) approximately 2700.
Furthermore, we derive that the growth rate of the small-scale magnetic field
for a general type of turbulence is Gamma ~ Re^((1-theta)/(1+theta)) in the
limit of infinite magnetic Prandtl numbers. For decreasing magnetic Prandtl
number (down to Pm approximately larger than 10), the growth rate of the
small-scale dynamo decreases. The details of this drop depend on the
WKB-approximation, which becomes invalid for a magnetic Prandtl number of about
unity.Comment: 13 pages, 8 figures; published in Phys. Rev. E 201
Stochastic Flux-Freezing and Magnetic Dynamo
We argue that magnetic flux-conservation in turbulent plasmas at high
magnetic Reynolds numbers neither holds in the conventional sense nor is
entirely broken, but instead is valid in a novel statistical sense associated
to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The
latter phenomenon is due to the explosive separation of particles undergoing
turbulent Richardson diffusion, which leads to a breakdown of Laplacian
determinism for classical dynamics. We discuss empirical evidence for
spontaneous stochasticity, including our own new numerical results. We then use
a Lagrangian path-integral approach to establish stochastic flux-freezing for
resistive hydromagnetic equations and to argue, based on the properties of
Richardson diffusion, that flux-conservation must remain stochastic at infinite
magnetic Reynolds number. As an important application of these results we
consider the kinematic, fluctuation dynamo in non-helical, incompressible
turbulence at unit magnetic Prandtl number. We present results on the
Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate
a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of
field-line motion is an essential ingredient of both. We finally consider
briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure
Reconnection in a Weakly Stochastic Field
We examine the effect of weak, small scale magnetic field structure on the
rate of reconnection in a strongly magnetized plasma. This affects the rate of
reconnection by reducing the transverse scale for reconnection flows, and by
allowing many independent flux reconnection events to occur simultaneously.
Allowing only for the first effect and using Goldreich and Sridhar's model of
strong turbulence in a magnetized plasma with negligible intermittency, we find
that the lower limit for the reconnection speed is the Alfven speed times the
Lundquist number to the power (-3/16). The upper limit on the reconnection
speed is typically a large fraction of Alfven speed. We argue that generic
reconnection in turbulent plasmas will normally occur at close to this upper
limit. The fraction of magnetic energy that goes directly into electron heating
scales as Lundquist number to the power (-2/5) and the thickness of the current
sheet scales as the Lundquist number to the power (-3/5). A significant
fraction of the magnetic energy goes into high frequency Alfven waves. We claim
that the qualitative sense of these conclusions, that reconnection is fast even
though current sheets are narrow, is almost independent of the local physics of
reconnection and the nature of the turbulent cascade. As the consequence of
this the Galactic and Solar dynamos are generically fast, i.e. do not depend on
the plasma resistivity.Comment: Extended version accepted to ApJ, 44pages, 2 figure
Rolling Friction in Loose Media and its Role in Mechanics Problems
Rolling friction between particles is to be set in problems of granular material mechanics alongside with sliding friction. A classical problem of material passive lateral pressure on the retaining wall is submitted as a case in point. 3D method of discrete elements was employed for numerical analysis. Material is a universe of spherical particles with specified size distribution. Viscose-elastic properties of the material and surface friction are included, when choosing contact forces. Particles' resistance to rolling relative to other particles and to the boundary is set into the model. Kinetic patterns of medium deformations are given. It has been proved that rolling friction can significantly affect magnitude and nature of passive lateral pressure on the retaining wall
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