Stanislav Boldyrev

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 shear-Alfvén fluid and magnetic-field fluctuations at each scale lambda become effectively aligned within the angle phi(lambda) proportional to lambda (1/4), which leads to scale-dependent depletion of the nonlinear interaction and to the field-perpendicular energy spectrum E(k(perpendicular)) proportional to k(perpendicular)(-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.

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 Ek ~ k-1.74. This result agrees well with recent numerical findings by Padoan & Nordlund and reproduces the observational Larson law u ~ l0.74...0.76. The application of the model to more general dissipative structures with higher fractal dimensionality is discussed.

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) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that 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.

Nature of Subproton Scale Turbulence in the Solar Wind

The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfvén turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfvén turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. These results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfvén turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

Scaling Relations of Supersonic Turbulence in Star-forming Molecular Clouds

We present a direct numerical and analytical study of driven supersonic magnetohydrodynamic 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 Ek ~ k-1.74, and the velocity difference scales as |Δu| ~ L0.42. The results agree well with the Kolmogorov-Burgers analytical model suggested for supersonic turbulence.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].

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 lambda approximately as theta(lambda) is proportional to lambda(1/4). This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) is proportional to k(-3/2) that is observed in numerical experiments of strongly magnetized turbulence.

SPECTRUM OF KINETIC-ALFVEN TURBULENCE

A numerical study of strong kinetic-Alfven turbulence at scales smaller than the ion gyroscale is presented, and a phenomenological model is proposed that argues that magnetic and density fluctuations are concentrated mostly in two-dimensional structures, which leads to their Fourier energy spectra E(k ){proportional_to}k {sup -8/3} , where k is the wavevector component normal to the strong background magnetic field. The results may provide an explanation for recent observations of magnetic and density fluctuations in the solar wind at sub-proton scales.

Structure function scaling in compressible super-Alfvénic 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 the arbitrary sonic Mach number, M(S). 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 M(S). Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations.

Supersonic Turbulence and Structure of Interstellar Molecular Clouds

The interstellar medium provides a unique laboratory for highly supersonic, driven hydrodynamic turbulence. We propose a theory of such turbulence, test it by numerical simulations, and use the results to explain observational scaling properties of interstellar molecular clouds, the regions where stars are born.

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 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.