arXiv subjects

Stanislav Boldyrev

Publications and source records attributed to Stanislav Boldyrev.

85 records · Page 5Linked to original sources

arXiv2005

Magnetic-field generation in helical turbulence

We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and magnetic helicity can be found as eigenmodes of a self-adjoint, Schrödinger-type system of evolution equations. We argue that large-scale and small-scale magnetic fluctuations cannot be effectively separated, and that the conventional alpha-model is, in general, not an adequate description of the large-scale dynamo mechanism. As a consequence, the correct numerical modeling of such processes should resolve magnetic fluctuations down to the very small, resistive scales.

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arXiv2005

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)].

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arXiv2005

On the Spectrum of Magnetohydrodynamic Turbulence

We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic field increases, which makes turbulence strong at all scales. To explain the weakening of the interaction, we propose that small-scale fluctuations of the velocity and magnetic fields become increasingly dynamically aligned as their scale decreases, so that turbulent eddies become locally anisotropic in the plane perpendicular to the large-scale magnetic field. In the limit of weak anisotropy, that is, weak large-scale magnetic field, our model reproduces the Goldreich-Sridhar spectrum, while the limit of strong anisotropy, that is, strong large-scale magnetic field, corresponds to the Iroshnikov-Kraichnan scaling of the spectrum. This is in good agreement with recent numerical results.

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arXiv2004

Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence

Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this letter we propose a unified approach for obtaining the velocity scaling in compressible and super--Alfvénic turbulence, valid for arbitrary sonic Mach number, \ms. We demonstrate with numerical simulations that the scaling can be described with the She--Lévêque formalism, where only one parameter, interpreted as the Hausdorff dimension of the most intense dissipative structures, needs to be varied as a function of \ms. Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations.

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arXiv2003

On magnetic field generation in Kolmogorov turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) ~ l^alpha, alpha<1. We propose that in the limit of small magnetic Prandtl number, i.e. when ohmic resistivity is much larger than viscosity, the smaller the roughness exponent, alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.

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arXiv2003

Levy model for interstellar scintillations

Observations of radio signals from distant pulsars provide a valuable tool for investigation of interstellar turbulence. The time-shapes of the signals are the result of pulse broadening by the fluctuating electron density in the interstellar medium. While the scaling of the shapes with the signal frequency is well understood, the observed anomalous scaling with respect to the pulsar distance has remained a puzzle for more than 30 years. We propose a new model for interstellar electron density fluctuations, which explains the observed scaling relations. We suggest that these fluctuations obey Levy statistics rather than Gaussian statistics, as assumed in previous treatments of interstellar scintillations.

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arXiv2002

Structure Function Scaling in the Taurus and Perseus Molecular Cloud Complexes

We compute the structure function scaling of the integrated intensity images of two J=1-0 13CO maps of Taurus and Perseus. The scaling exponents of the structure functions follow the velocity scaling of supersonic turbulence, suggesting that turbulence plays an important role in the fragmentation of cold interstellar clouds. The data also allows to verify the validity of the two basic assumptions of the hierarchical symmetry model, originally proposed for the derivation of the velocity structure function scaling. This shows that the same hierarchical symmetry holds for the projected density field of cold interstellar clouds.

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arXiv2002

Scintillations and Levy flights through the interstellar medium

Temporal broadening of pulsar signals results from electron density fluctuations in the interstellar medium that cause the radiation to travel along paths of different lengths. The Gaussian theory of fluctuations predicts that the pulse temporal broadening should scale with the wavelength as lambda^4, and with the dispersion measure (corresponding to distance to the pulsar) as DM^2. For large dispersion measure, DM > 20 pc/cm^3, the observed scaling is lambda^4 DM^4, contradicting the conventional theory. Although the problem has existed for 30 years, there has been no resolution to this paradox. We suggest that scintillations for distant pulsars are caused by non-Gaussian, spatially intermittent density fluctuations with a power-like probability distribution. This probability distribution does not have a second moment in a large range of density fluctuations, and therefore the previously applied conventional Fokker-Planck theory does not hold. Instead, we propose to apply the theory of Levy distributions (so-called Levy flights). Using the scaling analysis (confirmed by numerical simulations of ray propagation) we show that the observed scaling is recovered for large DM, if the density differences, delta N, have Levy distribution decaying as |delta N|^{-5/3}.

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arXiv2002

Supersonic turbulence and structure of interstellar molecular clouds

The interstellar medium (ISM) provides a unique laboratory for highly supersonic, driven hydrodynamics turbulence. We present a theory of such turbulence, confirm it by numerical simulations, and use the results to explain observational properties of interstellar molecular clouds, the regions where stars are born.

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arXiv2002

Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers

The existence of a weak galactic magnetic field has been repeatedly confirmed by observational data. The origin of this field has not as yet been explained in a fully satisfactory way and represents one of the main challenges of the astrophysical dynamo theory. In both the galactic dynamo theory and the primordial-origin theory, a major influence is exerted by the small-scale magnetic fluctuations. This article is devoted to constructing a systematic second-order statistical theory of such small-scale fields. The statistics of these fields are studied in the kinematic approximation and for the case of large Prandtl numbers, which is relevant for the galactic and protogalactic plasma. The advecting velocity field is assumed to be Gaussian and short-time correlated. Theoretical understanding of this kinematic dynamo model is a necessary prerequisite for any prospective nonlinear dynamo theory. The theory is developed for an arbitrary degree of compressibility and formally in d dimensions, which generalizes the previously known results, elicits the structure of the solutions, and uncovers a number of new effects. The magnetic energy spectra are studied as they grow and spread over scales during the initial stage of the field amplification. Exact Green's-function solutions are obtained. The spectral theory is supplemented by the study of magnetic-field correlation functions in the configuration space, where the dynamo problem can be mapped onto a particular one-dimensional quantum-mechanical problem. The latter approach is most suitable for the description of the kinematic dynamo in the long-time limit, i.e. when the magnetic excitation has spread over all scales present in the system. A simple way of calculating the growth rates of the magnetic fields in this long-time limit is proposed.

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arXiv2001

Scaling relations of supersonic turbulence in star-forming molecular clouds

We present a direct numerical and analytical study of driven supersonic MHD turbulence that is believed to govern the dynamics of star-forming molecular clouds. We describe statistical properties of the turbulence by measuring the velocity difference structure functions up to the fifth order. In particular, the velocity power spectrum in the inertial range is found to be close to E(k) \~ k^{-1.74}, and the velocity difference scales as <|Δu|>~ L^{0.42}. The results agree well with the Kolmogorov--Burgers analytical model suggested for supersonic turbulence in [astro-ph/0108300]. We then generalize the model to more realistic, fractal structure of molecular clouds, and show that depending on the fractal dimension of a given molecular cloud, the theoretical value for the velocity spectrum spans the interval [-1.74 ... -1.89], while the corresponding window for the velocity difference scaling exponent is [0.42 ... 0.78].

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arXiv2001

Kolmogorov-Burgers Model for Star Forming Turbulence

The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the dissipative range it behaves as Burgers turbulence developing shock singularities. On the base of the She-Leveque analytical model we then predict the velocity power spectrum in the inertial range to be E_k ~ k^{-1.74}. This result reproduces the observational Larson law, ~ l^{0.74...0.76}, [Larson, MNRAS 194 (1981) 809] and agrees well with recent numerical findings by Padoan and Nordlund [astro-ph/0011465]. The application of the model to more general dissipative structures, with higher fractal dimensionality, leads to better agreement with recent observational results.

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arXiv2001

A Solvable Model for Nonlinear Mean Field Dynamo

We formulate a solvable model that describes generation and saturation of mean magnetic field in a dynamo with kinetic helicity, in the limit of large magnetic Prandtl number. This model is based on the assumption that the stochastic part of the velocity field is Gaussian and white in time (the Kazantsev-Kraichnan ensemble), while the regular part describing the back reaction of the magnetic field is chosen from balancing the viscous and Lorentz stresses in the MHD Navier-Stokes equation. The model provides an analytical explanation for previously obtained numerical results.

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