Field In Magnetohydrodynamic Turbulence Research Articles

Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence

In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ⟨|(u·∇)u|⟩, (where u is the velocity field) and turbulent drag, but strengthening of the velocity field in MHD turbulence. We verify the above using shell model simulations of hydrodynamic and MHD turbulence. Quasi-static MHD turbulence too exhibits turbulent drag reduction similar to MHD turbulence.

CHARACTERISTIC LENGTHS OF MAGNETIC FIELD IN MAGNETOHYDRODYNAMIC TURBULENCE

In the framework of turbulence dynamo, flow motions amplify a weak seed magnetic field through the stretching of field lines. Although the amplification process has been a topic of active research, less attention has been paid to the length scales of magnetic field. In this paper, we described a numerical study on characteristic lengths of magnetic field in magnetohydrodynamic turbulence. We considered the case of very weak or zero mean magnetic field, which is applicable to the turbulence in the intergalactic space. Our findings are as follows. (1) At saturation, the peak of magnetic field spectrum occurs at $\sim L_0/2$, where $L_0$ is the energy injection scale, while the most energy containing scale is $\sim L_0/5$. The peak scale of spectrum of projected, two-dimensional field is $\sim L_0$. (2) During the stage of magnetic field amplification, the energy equipartition scale shows a power-law increase of $\sim t^{1.5}$, while the integral and curvature scales show a linear increase. The equipartition, integral, and curvature scales saturate at $\sim L_0$, $\sim 0.3L_0$, and $\sim 0.15L_0$, respectively. (3) The coherence length of magnetic field defined in the Faraday rotation measure (RM) due to the intergalactic magnetic field (IGMF) is related to the integral scale. We presented a formula that expresses the standard deviation of RM, $\sigma_{RM}$, in terms of the integral scale and rms strength of the IGMF, and estimated that $\sigma_{RM}$ would be $\sim 100$ and $\sim$ a few rad m$^{-2}$ for clusters and filaments, respectively.

Rapid Alignment of Velocity and Magnetic Field in Magnetohydrodynamic Turbulence

We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters and is seen both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between magnetic field and gradients of either pressure or kinetic energy, and is similar to alignment of velocity and vorticity in Navier-Stokes turbulence. This rapid and robust relaxation process leads to a local weakening of nonlinear terms.

Turbulent transport coefficients and residual energy in mean-field dynamo theory

The turbulent electromotive force in the mean-field equation needs to be modeled to predict a large-scale magnetic field in magnetohydrodynamic turbulence at high Reynolds number. Using a statistical theory for inhomogeneous turbulence, model expressions for transport coefficients appearing in the turbulent electromotive force are derived including the α coefficient and the turbulent diffusivity. In particular, as one of the dynamo effects, the pumping effect is investigated and a model expression for the pumping term is obtained. It is shown that the pumping velocity is closely related to the gradient of the turbulent residual energy, or the difference between the turbulent kinetic and magnetic energies. The production terms in the transport equation for the turbulent electromotive force are also examined and the validity of the model expression is assessed by comparing with earlier results concerning the isotropic α coefficient. The mean magnetic field in a rotating spherical shell is calculated using a turbulence model to demonstrate the pumping effect.

Test Particle Energization by Current Sheets and Nonuniform Fields in Magnetohydrodynamic Turbulence

We perform numerical experiments of test particle energization in turbulent magnetic and electric fields obtained from pseudospectral direct numerical solutions of compressible three-dimensional magnetohydrodynamic (MHD) equations with a strong background magnetic field. The natural tendency of turbulent MHD fields is to form current sheets along the magnetic field direction, as well as strong nonuniform fields in the transverse directions. By associating the MHD dissipation length scale with the ion inertial scale, we found differential energization in parallel and perpendicular directions according to the type of particles considered. Electrons develop large parallel velocities, especially in current sheets. Protons instead show higher perpendicular energization due to the nonuniform perpendicular induced electric field produced by the plasma MHD velocity, which varies on proton length scales. Implications for dissipation mechanisms in a coronal heating model are discussed.