arXiv subjects
Stanislav Boldyrev
Publications and source records attributed to Stanislav Boldyrev.
Magnetic dynamo action in random flows with zero and finite correlation times
Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible, non-helical, homogeneous and isotropic flow. In the Kazantsev dynamo model the statistics of the driving flow are assumed to be instantaneously correlated in time. Here we compare the results of the model with the dynamo properties of a simulated flow that has equivalent spatial characteristics as the Kazantsev flow but different temporal statistics. In particular, the simulated flow is a solution of the forced Navier-Stokes equations and hence has a finite correlation time. We find that the Kazantsev model typically predicts a larger magnetic growth rate and a magnetic spectrum that peaks at smaller scales. However, we show that by filtering the diffusivity spectrum at small scales it is possible to bring the growth rates into agreement and simultaneously align the magnetic spectra.
Magnetic dynamo action at low magnetic Prandtl numbers
Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.
Strong magnetohydrodynamic turbulence with cross helicity
Magnetohydrodynamics (MHD) provides the simplest description of magnetic plasma turbulence in a variety of astrophysical and laboratory systems. MHD turbulence with nonzero cross helicity is often called imbalanced, as it implies that the energies of Alfvén fluctuations propagating parallel and anti-parallel the background field are not equal. Recent analytical and numerical studies have revealed that at every scale, MHD turbulence consists of regions of positive and negative cross helicity, indicating that such turbulence is inherently locally imbalanced. In this paper, results from high resolution numerical simulations of steady-state incompressible MHD turbulence, with and without cross helicity are presented. It is argued that the inertial range scaling of the energy spectra (E^+ and E^-) of fluctuations moving in opposite directions is independent of the amount of cross-helicity. When cross helicity is nonzero, E^+ and E^- maintain the same scaling, but have differing amplitudes depending on the amount of cross-helicity.
Numerical simulations of imbalanced strong magnetohydrodynamic turbulence
Magnetohydrodynamics (MHD) is invoked to address turbulent fluctuations in a variety of astrophysical systems. MHD turbulence in nature is often anisotropic and imbalanced, in that Alfvenic fluctuations moving in opposite directions along the background magnetic field carry unequal energies. This work formulates specific requirements for effective numerical simulations of strong imbalanced MHD turbulence with a guide field B0 High-resolution simulations are then performed and they suggest that the spectra of the counter-propagating Alfven modes do not differ from the balanced case, while their amplitudes and the corresponding rates of energy cascades are significantly affected by the imbalance. It is further proposed that the stronger the imbalance the larger the magnetic Reynolds number that is required in numerical simulations in order to correctly reproduce the turbulence spectrum. This may explain current discrepancies among numerical simulations and observations of imbalanced MHD turbulence.
Spectrum of weak magnetohydrodynamic turbulence
Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or non-balanced, in that the energies of Afvén waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy $E_v-E_b$ at small field-parallel wave numbers. As a result, the energy spectra of counter-propagating Alfvén waves are not scale-invariant. In the limit of infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling $E(k)\propto k_{\perp}^{-2}$. The generation of condensate is apparently related to the breakdown of mirror symmetry in non-balanced turbulence.
Dynamic Alignment and Exact Scaling Laws in MHD Turbulence
Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical systems. Recent high-resolution numerical simulations suggest that the energy spectrum of strong incompressible MHD turbulence is $E(k_{\perp})\propto k_{\perp}^{-3/2}$. So far, there has been no phenomenological theory that simultaneously explains this spectrum and satisfies the exact analytic relations for MHD turbulence due to Politano & Pouquet. Indeed, the Politano-Pouquet relations are often invoked to suggest that the spectrum of MHD turbulence instead has the Kolmogorov scaling -5/3. Using geometrical arguments and numerical tests, here we analyze this seeming contradiction and demonstrate that the -3/2 scaling and the Politano-Pouquet relations are reconciled by the phenomenon of scale-dependent dynamic alignment that was recently discovered in MHD turbulence.
Magnetic dynamo action in astrophysical turbulence
We investigate the structure of magnetic field amplified by turbulent velocity fluctuations, in the framework of the kinematic Kazantsev-Kraichnan model. We consider Kolmogorov distribution of velocity fluctuations, and assume that both Reynolds number and magnetic Reynolds number are very large. We present the full numerical solution of the model for the spectra and the growth rates of magnetic fluctuations. We consider astrophysically relevant limits of large and small magnetic Prandtl numbers, and address both helical and nonhelical cases.
Role of cross helicity in magnetohydrodynamic turbulence
Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in imbalanced regions where cross-helicity is non-zero. When averaged over regions of positive and negative cross-helicity, the result is consistent with the simulations of balanced turbulence. An analytical explanation for the obtained results is proposed.
Analog of Astrophysical Magnetorotational Instability in a Couette-Taylor Flow of Polymer Fluids
We report experimental observation of an instability in a Couette-Taylor flow of a polymer fluid in a thin gap between two coaxially rotating cylinders in a regime where their angular velocity decreases with the radius while the specific angular momentum increases with the radius. In the considered regime, neither the inertial Rayleigh instability nor the purely elastic instability are possible. We propose that the observed "elasto-rotational" instability is an analog of the magnetorotational instability which plays a fundamental role in astrophysical Keplerian accretion disks.
Amplification of magnetic fields by dynamo action in Gaussian-correlated helical turbulence
We investigate the growth and structure of magnetic fields amplified by kinematic dynamo action in turbulence with non-zero kinetic helicity. We assume a simple Gaussian velocity correlation tensor, which allows us to consider very large magnetic Reynolds numbers, up to one trillion. We use the kinematic Kazantsev-Kraichnan model of dynamo and find a complete numerical solution for the correlation functions of growing magnetic fields.
Magnetic dynamo action in helical turbulence
We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model. We present the numerical solution of the model for the practically important case of Kolmogorov distribution of velocity fluctuations, with a large magnetic Reynolds number. We find that in contrast to the nonhelical case where growing magnetic fields are described by a few bound eigenmodes concentrated inside the inertial interval of the velocity field, in the helical case the number of bound eigenmodes considerably increases; moreover, new unbound eigenmodes appear. Both bound and unbound eigenmodes contribute to the large-scale magnetic field. This indicates a limited applicability of the conventional alpha model of a large-scale dynamo action, which captures only unbound modes.
On weak and strong magnetohydrodynamic turbulence
Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_λ$ the fluctuating field at the scale $λ\sim 1/k_{\perp}$. We find that when the critical balance condition, $k_{\|}B_0\sim k_{\perp} b_λ$, is satisfied, the turbulence is strong, and the energy spectrum is $E(k_{\perp})\propto k^{-3/2}_{\perp}$. As the $k_{\|}$ width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit $k_{\|}B_0\gg k_{\perp} b_λ$, the spectrum approaches $E(k_{\perp})\propto k_{\perp}^{-2}$. The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled.
Numerical Measurements of the Spectrum in Magnetohydrodynamic Turbulence
We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic turbulence with a strong guide field. The aim is to resolve the controversy regarding the power law exponent (α, say) of the field perpendicular energy spectrum E(k_\perp) \propto k_\perp ^ α. The two main theoretical predictions, α=-3/2 and α=-5/3, have both received some support from numerical simulations carried out by different groups. Our simulations have a resolution of 512^3 mesh points, a strong guide field, an anisotropic simulation domain, and implement a broad range of large-scale forcing routines, including those previously reported in the literature. Our findings indicate that the spectrum of well developed, strong incompressible MHD turbulence with a strong guide field is E(k_{\perp})\propto k_{\perp}^{-3/2}.
Dynamic Alignment in Driven Magnetohydrodynamic Turbulence
Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale λapproximately as θ_λ~ λ^{1/4}. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) ~ k^{-3/2} that is observed in numerical experiments of strongly magnetized turbulence.
Spectrum of magnetohydrodynamic turbulence
We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached, it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of fluid and magnetic-field fluctuations at each scale $λ$ become effectively aligned within the angle $ϕ_λ\propto λ^{1/4}$, which leads to scale-dependent depletion of nonlinear interaction and to the field-perpendicular energy spectrum $E(k_{\perp})\propto k_{\perp}^{-3/2}$. Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.
Non-Gaussian Radio-Wave Scattering in the Interstellar Medium
It was recently suggested by Boldyrev & Gwinn that the characteristics of radio scintillations from distant pulsars are best understood if the interstellar electron-density fluctuations that cause the time broadening of the radio pulses obey non-Gaussian statistics. In this picture the density fluctuations are inferred to be strong on very small scales ($\sim 10^8-10^{10} {cm}$). We argue that such density structures could correspond to the ionized boundaries of molecular regions (clouds) and demonstrate that the power-law distribution of scattering angles that is required to match the observations arises naturally from the expected intersections of our line of sight with randomly distributed, thin, approximately spherical ionized shells of this type. We show that the observed change in the time-broadening behavior for pulsar dispersion measures $\lesssim 30 {\rm pc} {\rm cm}^{-3}$ is consistent with the expected effect of the general ISM turbulence, which should dominate the scattering for nearby pulsars. We also point out that if the clouds are ionized by nearby stars, then their boundaries may become turbulent on account of an ionization front instability. This turbulence could be an alternative cause of the inferred density structures. An additional effect that might contribute to the strength of the small-scale fluctuations in this case is the expected flattening of the turbulent density spectrum when the eddy sizes approach the proton gyroscale.
Turbulent Origin of the Galactic-Center Magnetic Field: Nonthermal Radio Filaments
A great deal of study has been carried out over the last twenty years on the origin of the magnetic activity in the Galactic center. One of the most popular hypotheses assumes milli-Gauss magnetic field with poloidal geometry, pervading the inner few hundred parsecs of the Galactic-center region. However, there is a growing observational evidence for the large-scale distribution of a much weaker field of B \lesssim 10 micro G in this region. Here, we propose that the Galactic-center magnetic field originates from turbulent activity that is known to be extreme in the central hundred parsecs. In this picture the spatial distribution of the magnetic field energy is highly intermittent, and the regions of strong field have filamentary structures. We propose that the observed nonthermal radio filaments appear in (or, possibly, may be identified with) such strongly magnetized regions. At the same time, the large-scale diffuse magnetic field is weak. Both results of our model can explain the magnetic field measurements of the the Galactic-center region. In addition, we discuss the role of ionized outflow from stellar clusters in producing the long magnetized filaments perpendicular to the Galactic plane.