Simulations of the Small-Scale Turbulent Dynamo

By A. Schekochihin, S. Cowley, Samuel F. Taylor, J. Maron, James C. McWilliams. 2003

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We report the results of an extensive numerical study of the small-scale turbulent dynamo. The primary focus is on the case of large magnetic Prandtl numbers Prm, which is relevant for hot low-density astrophysical plasmas. A Prm parameter scan is given for the model case of viscosity-dominated (low Reynolds number) turbulence. We concentrate on three topics: magnetic energy spectra and saturation levels, the structure of the magnetic field lines, and intermittency of the field strength distribution. The main results are as follows: (1) the folded structure of the field (direction reversals at the resistive scale, field lines curved at the scale of the flow) persists from the kinematic to the nonlinear regime; (2) the field distribution is self-similar and appears to be lognormal during the kinematic regime and exponential in the saturated state; and (3) the bulk of the magnetic energy is at the resistive scale in the kinematic regime and remains there after saturation, although the magnetic energy spectrum becomes much shallower. We propose an analytical model of saturation based on the idea of partial two-dimensionalization of the velocity gradients with respect to the local direction of the magnetic folds. The model-predicted saturated spectra are in excellent agreement with numerical results. Comparisons with large-Re, moderate-Prm runs are carried out to confirm the relevance of these results and to test heuristic scenarios of dynamo saturation. New features at large Re are elongation of the folds in the nonlinear regime from the viscous scale to the box scale and the presence of an intermediate nonlinear stage of slower than exponential magnetic energy growth accompanied by an increase of the resistive scale and partial suppression of the kinetic energy spectrum in the inertial range. Numerical results for the saturated state do not support scale-by-scale equipartition between magnetic and kinetic energies, with a definite excess of magnetic energy at small scales. A physical picture of the saturated state is proposed.

Subfields: Astronomy and Astrophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/e76bbac12626568ab4c2acc2e86b6e40543bb3c5

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Citations in the corpus

Evolving turbulence and magnetic fields in galaxy clusters (2005, background): “The value of Rm in those simulations is about 1000, so the deviation from the scaling kB ∼ k η ∝ R−1/2m advocated by Schekochihin et al. (2004) is by a factor of 3–5 over the range Rm = 400–1000.”
X-ray Spectroscopy of Cooling Clusters (2005, background): “The diffuse hot ionized plasma in clusters is magnetized which means that MHD processes may be important (Schekochihin et al. 2004).”
The Case for a Distributed Solar Dynamo Shaped by Near-Surface Shear (2005, background): “At small magnetic Prandtl number the small scale dynamo is much harder to excite (Schekochihin et al. 2004a, Boldyrev & Cattaneo 2004, Haugen et al. 2004) and may become subdominant, allowing the large scale dynamo effect to become more prominent.”
NUMERICAL SIMULATIONS OF QUIET SUN MAGNETISM: ON THE CONTRIBUTION FROM A SMALL-SCALE DYNAMO (2014, methodology): “While the regime PM > 1 has been studied in great detail including the non-linear saturation phase (Schekochihin et al. 2004), the regime PM 1 is less accessible by direct numerical simulations.”
MAGNETIC WREATHS AND CYCLES IN CONVECTIVE DYNAMOS (2012, background): “For high Pm dynamos, the resistive scale is smaller than the viscous scale, which tends to promote the growth of magnetic energy at small scales (e.g., Schekochihin et al. 2004).”
MHD simulations of the magnetorotational instability in a shearing box with zero net flux II. The effect of transport coefficients (2007, background): “Indeed, as argued by Schekochihin et al. (2004) for the kinematic regime, the visous dissipation length and the resistive dissipation length are related through lν ∼ Pm1/2lη (this relation, not taking rotation into account, is not strictly speaking applicable, but may be indicative).”
Accretion disc viscosity: how big is alpha? (2007, background): “(Schekochihin et al. 2004, 2005) discuss this mainly for the interstellar medium.”
A NEW JEANS RESOLUTION CRITERION FOR (M)HD SIMULATIONS OF SELF-GRAVITATING GAS: APPLICATION TO MAGNETIC FIELD AMPLIFICATION BY GRAVITY-DRIVEN TURBULENCE (2011, background): “The numerical values of Re and Rm are thus related to the grid resolution and to how well the turbulent motions are resolved (e.g., Haugen et al. 2004; Balsara et al. 2004; Schekochihin et al. 2004).”
Small-scale dynamo action during the formation of the first stars and galaxies - I. The ideal MHD limit (2010, background): “This property has been discussed in detail by Schekochihin et al. (2004); Brandenburg & Subramanian (2005).”
THE GENERATION OF STRONG MAGNETIC FIELDS DURING THE FORMATION OF THE FIRST STARS (2010, methodology): “…dynamo have been explored both in numerical simulations of driven turbulence without self-gravity and in analytic models (Haugen et al. 2004; Schekochihin et al. 2004; Brandenburg & Subramanian 2005), as well as in cosmological simulations of magnetic field generation in 1 Zentrum für…”
ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS (2007, background): “…scale, while the scale of the field-direction reversals transverse to the fold is determined by the dissipation physics: in MHD with isotropic viscosity and resistivity, it is the resistive scale.11 Although Alfvén waves propagating along the folds may exist (Schekochihin et al. 2004; spectrum.”
NONTHERMAL RADIATION OF YOUNG SUPERNOVA REMNANTS: THE CASE OF RX J1713.7−3946 (2010, background): “It reveals the exponential tails when the magnetic field is amplified by turbulent motions (see Schekochihin et al. 2004).”
Cosmic ray transport in galaxy clusters: implications for radio halos, gamma-ray signatures, and cool core heating (2010, background): “How this changes due to nonlinear effects is not yet fully clear (For papers on this aspect see Haugen et al. 2004; Schekochihin et al. 2004; Brandenburg & Subramanian 2005).”