3,444 research outputs found
On geometric properties of passive random advection
We study geometric properties of a random Gaussian short-time correlated
velocity field by considering statistics of a passively advected metric tensor.
That describes universal properties of fluctuations of tensor objects frozen
into the fluid and passively advected by it. The problem of one-point
statistics of co- and contravariant tensors is solved exactly, provided the
advected fields do not reach dissipative scales, which would break the symmetry
of the problem. Asymptotic in time duality of the problem is established, which
in the three-dimensional case relates the probabilities of the volume
deformations into "tubes" and into "sheets".Comment: latex, 8 page
Burgers turbulence with pressure
The randomly driven Burgers equation with pressure is considered as a 1D
model of strong turbulence of compressible fluid. It is shown that infinitely
small pressure provides a finite effect on the velocity and density statistics
and this case therefore is qualitatively different from turbulence without
pressure. We establish the corresponding operator product expansion and predict
the intermittent velocity- difference and mass-difference PDFs. We then apply
the developed methods to the statistics of a passive scalar advected by the
Burgers field.Comment: 4 pages, revte
Simulation of Relativistic Force-free Magnetohydrodynamic Turbulence
We present numerical studies of 3-dimensional magnetohydrodynamic (MHD)
turbulence in a strongly magnetized medium in the extremely relativistic limit,
in which the inertia of the charge carriers can be neglected. We have focused
on strong Alfvenic turbulence in the limit. We have found the following
results. First, the energy spectrum is consistent with a Kolmogorov spectrum:
. Second, turbulence shows a Goldreich-Sridhar type
anisotropy: , where and
are wavenumbers along and perpendicular to the local mean magnetic field
directions, respectively. These scalings are in agreement with earlier
theoretical predictions by Thompson & Blaes.Comment: 4 pages; 3 figures; APJL, submitte
Radio-wave propagation in the non-Gaussian interstellar medium
Radio waves propagating from distant pulsars in the interstellar medium
(ISM), are refracted by electron density inhomogeneities, so that the intensity
of observed pulses fluctuates with time. The theory relating the observed pulse
time-shapes to the electron-density correlation function has developed for 30
years, however, two puzzles have remained. First, observational scaling of
pulse broadening with the pulsar distance is anomalously strong; it is
consistent with the standard model only when non-uniform statistics of electron
fluctuations along the line of sight are assumed. Second, the observed pulse
shapes are consistent with the standard model only when the scattering material
is concentrated in a narrow slab between the pulsar and the Earth.
We propose that both paradoxes are resolved at once if one assumes stationary
and uniform, but non-Gaussian statistics of the electron-density distribution.
Such statistics must be of Levy type, and the propagating ray should exhibit a
Levy flight. We propose that a natural realization of such statistics may be
provided by the interstellar medium with random electron-density
discontinuities. We develop a theory of wave propagation in such a non-Gaussian
random medium, and demonstrate its good agreement with observations. The
qualitative introduction of the approach and the resolution of the
anomalous-scaling paradox was presented earlier in [PRL 91, 131101 (2003); ApJ
584, 791 (2003)].Comment: 27 pages, changes to match published versio
Ion-scale spectral break of solar wind turbulence at high and low beta
The power spectrum of magnetic fluctuations in the solar wind at 1 AU displays a break between two power laws in the range of spacecraft-frame frequencies 0.1 to 1 Hz. These frequencies correspond to spatial scales in the plasma frame near the proton gyroradius ρi and proton inertial length di. At 1 AU it is difficult to determine which of these is associated with the break, since [Formula: see text] and the perpendicular ion plasma beta is typically β⊥i∼1. To address this, several exceptional intervals with β⊥i≪1 and β⊥i≫1 were investigated, during which these scales were well separated. It was found that for β⊥i≪1 the break occurs at di and for β⊥i≫1 at ρi, i.e., the larger of the two scales. Possible explanations for these results are discussed, including Alfvén wave dispersion, damping, and current sheets
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