Role of helicities for the dynamics of turbulent magnetic fields

Investigations of the inverse cascade of magnetic helicity are conducted with pseudospectral, three-dimensional direct numerical simulations of forced and decaying incompressible magnetohydrodynamic turbulence. The high-resolution simulations which allow for the necessary scale-separation show that the observed self-similar scaling behavior of magnetic helicity and related quantities can only be understood by taking the full nonlinear interplay of velocity and magnetic fluctuations into account. With the help of the eddy-damped quasi-normal Markovian approximation a probably universal relation between kinetic and magnetic helicities is derived that closely resembles the extended definition of the prominent dynamo pseudoscalar $\alpha$. This unexpected similarity suggests an additional nonlinear quenching mechanism of the current-helicity contribution to $\alpha$.Comment: 7 pages, 4 figures, This is an Author's Accepted Manuscript of an article published in Geophysical \& Astrophysical Fluid Dynamics, First Published online : 01 Jun 2012. [copyright Taylor \& Francis

Large-scale Magnetic Structure Formation in 3D-MHD Turbulence

The inverse cascade of magnetic helicity in 3D-MHD turbulence is believed to be one of the processes responsible for large scale magnetic structure formation in astrophysical systems. In this work we present an exhaustive set of high resolution direct numerical simulations (DNS) of both forced and decaying 3D-MHD turbulence, to understand this structure formation process. It is first shown that an inverse cascade of magnetic helicity in small-scale driven turbulence does not necessarily generate coherent large-scale magnetic structures. The observed large-scale magnetic field, in this case, is severely perturbed by magnetic fluctuations generated by the small-scale forcing. In the decaying case, coherent large-scale structure form similar to those observed astronomically. Based on the numerical results the formation of large-scale magnetic structures in some astrophysical systems, is suggested to be the consequence of an initial forcing which imparts the necessary turbulent energy into the system, which, after the forcing shuts off, decays to form the large-scale structures. This idea is supported by representative examples e.g. cluster of galaxies.Comment: 21 pages in emulateapj format. 29 figures and 1 table. Accepted for publication in APJ on 11/09/201

Alfv\'en-dynamo balance and magnetic excess in MHD turbulence

3D Magnetohydrodynamic (MHD) turbulent flows with initially magnetic and kinetic energies at equipartition spontaneously develop a magnetic excess (or residual energy), as well in numerical simulations and in the solar wind. Closure equations obtained in 1983 describe the residual spectrum as being produced by a dynamo source proportional to the total energy spectrum, balanced by a linear Alfv\'en damping term. A good agreement was found in 2005 with incompressible simulations; however, recent solar wind measurements disagree with these results. The previous dynamo-Alfv\'en theory is generalized to a family of models, leading to simple relations between residual and total energy spectra. We want to assess these models in detail against MHD simulations and solar wind data. The family of models is tested against compressible decaying MHD simulations with low Mach number, low cross-helicity, zero mean magnetic field, without or with expansion terms (EBM or expanding box model). A single dynamo-Alfv\'en model is found to describe correctly both solar wind scalings and compressible simulations without or with expansion. It is equivalent to the 1983-2005 closure equation but with critical balance of nonlinear turnover and linear Alfv\'en times, while the dynamo source term remains unchanged. The discrepancy with previous incompressible simulations is elucidated. The model predicts a linear relation between the spectral slopes of total and residual energies $m_R = -1/2 + 3/2 m_T$. Examining the solar wind data as in \cite{2013ApJ...770..125C}, our relation is found to be valid whatever the cross-helicity, even better so at high cross-helicity, with the total energy slope varying from $1.7$ to $1.55$.Comment: 7 pages, 7 figures, accepted for publication in A&

Three-dimensional Iroshnikov-Kraichnan turbulence in a mean magnetic field

Forced, weak MHD turbulence with guide field is shown to adopt different regimes, depending on the magnetic excess of the large forced scales. When the magnetic excess is large enough, the classical perpendicular cascade with $5/3$ scaling is obtained, while when equipartition is imposed, an isotropic $3/2$ scaling appears in all directions with respect to the mean field (\cite{2010PhRvE..82b6406G} or GM10). We show here that the $3/2$ scaling of the GM10 regime is not ruled by a small-scale cross-helicity cascade, and propose that it is a 3D extension of a perpendicular weak Iroshnikov-Kraichnan (IK) cascade. We analyze in detail the structure functions in real space and show that they closely follow the critical balance relation both in the local frame and the global frame: we show that there is no contradiction between this and the isotropic $3/2$ scaling of the spectra. We propose a scenario explaining the spectral structure of the GM10 regime, that starts with a perpendicular weak IK cascade and extends to 3D by using quasi-resonant couplings. The quasi-resonance condition happens to reduce the energy flux in the same way as is done in the weak perpendicular cascade, so leading to a $3/2$ scaling in all directions. We discuss the possible applications of these findings to solar wind turbulence.Comment: Major re-write of manuscrip

The inverse cascade of magnetic helicity in magnetohydrodynamic turbulence

The nonlinear dynamics of magnetic helicity, $H^M$, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of $H^M$ is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. \textbf{77} 321 (1976)]. By revisiting this theory a universal dynamical balance relation is found that includes effects of kinetic helicity, as well as kinetic and magnetic energy on the inverse cascade of $H^M$ and explains the above-mentioned discrepancy. Considering the result in the context of mean-field dynamo theory suggests a nonlinear modification of the $\alpha$-dynamo effect important in the context of magnetic field excitation in turbulent plasmas.Comment: Minor corrections and improvements mad

Anisotropy of third-order structure functions in MHD turbulence

The measure of the third-order structure function, Y, is employed in the solar wind to compute the cascade rate of turbulence. In the absence of a mean field B0=0, Y is expected to be isotropic (radial) and independent of the direction of increments, so its measure yields directly the cascade rate. For turbulence with mean field, as in the solar wind, Y is expected to become more two dimensional (2D), that is, to have larger perpendicular components, loosing the above simple symmetry. To get the cascade rate one should compute the flux of Y, which is not feasible with single-spacecraft data, thus measurements rely upon assumptions about the unknown symmetry. We use direct numerical simulations (DNS) of magneto-hydrodynamic (MHD) turbulence to characterize the anisotropy of Y. We find that for strong guide field B0=5 the degree of two-dimensionalization depends on the relative importance of shear and pseudo polarizations (the two components of an Alfv\'en mode in incompressible MHD). The anisotropy also shows up in the inertial range. The more Y is 2D, the more the inertial range extent differs along parallel and perpendicular directions. We finally test the two methods employed in observations and find that the so-obtained cascade rate may depend on the angle between B0 and the direction of increments. Both methods yield a vanishing cascade rate along the parallel direction, contrary to observations, suggesting a weaker anisotropy of solar wind turbulence compared to our DNS. This could be due to a weaker mean field and/or to solar wind expansion.Comment: Some text editing and typos corrected, 13 pages, 6 figures, to be published in Ap

Emergence of magnetic structure in supersonic isothermal magnetohydrodynamic turbulence

The inverse transfer of magnetic helicity is a fundamental process which may explain large scale magnetic structure formation and sustainement. Until very recently, direct numerical simulations (DNS) of the inverse transfer in magnetohydrodynamics (MHD) turbulence have been done in incompressible MHD or at low Mach numbers only. We review first results obtained through DNS of the isothermal MHD equations at Mach numbers ranging from subsonic to about 10. The spectral exponent of the magnetic helicity spectrum becomes flatter with increasing compressibility. When considering the Alfv\'en velocity in place of the magnetic field however, results found in incompressible MHD, including a dynamic balance between shear and twist, can be extended to supersonic MHD. In the global picture of an inverse transfer of magnetic helicity, three phenomena are at work: a local direct transfer mediated by the large scale velocity field, a local inverse transfer mediated by the intermediate scale velocity field and a nonlocal inverse transfer mediated by the small scale velocity field. The compressive part of the velocity field is geometrically favored in the local direct transfer and contributes to the nonlocal inverse transfer, but plays no role in the local inverse transfer.Comment: Chapter in Helicities in Geophysics, Astrophysics and Beyond (AGU Books, Wiley, 2023 or 2024