Small-scale structures in three-dimensional magnetohydrodynamic turbulence

We investigate using direct numerical simulations with grids up to 1536(3) points, the rate at which small scales develop in a decaying three-dimensional MHD flow both for deterministic and random initial conditions. Parallel current and vorticity sheets form at the same spatial locations, and further destabilize and fold or roll up after an initial exponential phase. At high Reynolds numbers, a self-similar evolution of the current and vorticity maxima is found, in which they grow as a cubic power of time; the flow then reaches a finite dissipation rate independent of the Reynolds number.     

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ～ exp(?A|δX| ^μ ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.     

Scaling properties of fluctuations in stationary turbulence

Turbulent fluctuations are treated using a stationary distribution functionw _st for an order parameter field representing a fluid. Naive scale invariance ofw _st yields thek ^–5/3 spectral law in three dimensions andk ^–3 in two dimensions. The noise parameter of the stationary distribution is connected with energy flow or enstrophy conservation, respectively. In order to include fluctuations of the local energy dissipation a grand distribution function is introduced.     

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.     

Shell models of magnetohydrodynamic turbulence

Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models.     

Anisotropic scaling of magnetohydrodynamic turbulence

We present a quantitative estimate of the anisotropic power and scaling of magnetic field fluctuations in inertial range magnetohydrodynamic turbulence, using a novel wavelet technique applied to spacecraft measurements in the solar wind. We show for the first time that, when the local magnetic field direction is parallel to the flow, the spacecraft-frame spectrum has a spectral index near 2. This can be interpreted as the signature of a population of fluctuations in field-parallel wave numbers with a k(-2)_(||) spectrum but is also consistent with the presence of a "critical balance" style turbulent cascade. We also find, in common with previous studies, that most of the power is contained in wave vectors at large angles to the local magnetic field and that this component of the turbulence has a spectral index of 5/3.     

Scaling properties of the temperature field in convective turbulence

We report the scaling properties of temperature in turbulent convection in water. In the central region of the convection cell, we find that the peak frequency of the temperature dissipation spectra may be identified as the "Bolgiano frequency," with respect to which the temperature power spectra are universal functions; and that the usual inertial range is taken up entirely by the buoyancy subrange, so that a "high frequency" scaling subrange emerges only through an extended-self-similarity-type analysis. Moreover, the buoyancy subrange assumes the value of 2/5 predicted for the Bolgiano-Obukhov scaling only in the central region of the cell; in the mixing zone the exponent for the high frequency scaling exponent has a value of 2/3.     

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.     

Spectral energy dynamics in magnetohydrodynamic turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024(3) collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, E(R)k=|E(M)k - E(K)k|, and total energy, Ek=E(K)k+E(M)k, are observed to scale self-similarly in the inertial range as E(R)k approximately k(-7/3), E(k)approximately k(-5/3) (isotropic case) and E(R)(k(perpendicular) approximately k(-2)(perpendicular), E(k(perpendicular))approximately k(-3/2)(perpendicular) (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasinormal Markovian closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields E(R)k approximately kE2(k), which is confirmed by the simulations.     

Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k⁻¹ spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f (α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.     

Weak magnetohydrodynamic turbulence of a magnetized plasma

A weak turbulence of the magnetohydrodynamic waves in a strongly magnetized plasma was studied in the case when the plasma pressure is small as compared to the magnetic field pressure. In this case, the principal nonlinear mechanism is the resonance scattering of fast magnetoacoustic and Alfvén waves on slow magnetoacoustic waves. Since the former waves are high-frequency (HF) with respect to the latter, the total number of HF waves in the system is conserved (adiabatic invariant). In the weak turbulence regime, this integral of motion generates a Kolmogorov spectrum with a constant flux of the number of HF waves toward the longwave region. The shortwave region features a Kolmogorov spectrum with a constant energy flux. An exact angular dependence of the turbulence spectra is determined for the wave propagation angles close to the average magnetic field direction.     

Gravitational radiation from primordial helical magnetohydrodynamic turbulence

We consider gravitational waves (GWs) generated by primordial inverse-cascade helical magneto-hydrodynamical (MHD) turbulence produced by bubble collisions at the electroweak phase transitions (EWPT). Compared to the unmagnetized EWPT case, the spectrum of MHD-turbulence-generated GWs peaks at lower frequency with larger amplitude and can be detected by the proposed Laser Interferometer Space Antenna.     

On triple correlations in isotropic electronic magnetohydrodynamic turbulence

The evolution of the correlation characteristics in three-dimensional isotropic electronic magnetohydrodynamic turbulence is investigated. Universal exact relations between the longitudinal and longitudinal-transverse two-point triple correlations of the components of the fluctuational magnetic fields and the rates of dissipation of the magnetic helicity and energy are obtained in the inertial range. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 9, 626–630 (10 May 1999)     

Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wave number ranges in a Beta > or approximately = 1 plasma. The k(-5/3) inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At smaller wavelengths krho(i) > or = 1 the electric spectrum is enhanced and is consistent with the expected dispersion relation of short-wavelength kinetic Alfvén waves. Kinetic Alfvén waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluidlike nature of the solar wind.     

Weak compressible magnetohydrodynamic turbulence in the solar corona

This Letter presents a calculation of the power spectra of weakly turbulent Alfvén waves and fast magnetosonic waves ("fast waves") in low- plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfvén waves. High-frequency waves produced by MHD turbulence are a promising explanation for the anisotropic heating of minor ions in the solar corona.     

Energy decay laws in strongly anisotropic magnetohydrodynamic turbulence

We investigate the influence of a uniform magnetic field B(0)=B(0)e( parallel) on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along B(0) is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology of Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong B(0), with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.