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: $E(k)\sim k^{-5/3}$. Second, turbulence shows a Goldreich-Sridhar type anisotropy: $k_{\|} \propto k_{\perp}^{2/3}$, where $k_{\|}$ and $k_{\perp}$ 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