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Magnetohydrodynamic (MHD) turbulence is a cross-field process relevant to many systems. A prerequisite for understanding these systems is to constrain the role of MHD turbulence, and in particular, the energy exchange between kinetic and magnetic forms. The energetics of strongly magnetized and compressible turbulence has so far resisted attempts to understand them. Numerical simulations reveal that kinetic energy can be orders of magnitude higher than fluctuating magnetic energy. We solved this lack-of-balance puzzle by calculating the energetics of compressible and sub-Alfvénic turbulence based on the dynamics of coherent cylindrical fluid parcels. Using the MHD Lagrangian, we proved analytically that the bulk of the magnetic energy transferred to kinetic energy is the energy that is stored in the coupling between the ordered and fluctuating magnetic field. The analytical relations are in strikingly good agreement with numerical data, up to second-order terms.
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On the properties and implications of collapse-driven MHD turbulence
ABSTRACT We investigate the driving of MHD turbulence by gravitational contraction using simulations of an initially spherical, isothermal, magnetically supercritical molecular cloud core with transonic and trans-Alfvénic turbulence. We perform a Helmholtz decomposition of the velocity field, and investigate the evolution of its solenoidal and compressible parts, as well as of the velocity component along the gravitational acceleration vector, a proxy for the infall component of the velocity field. We find that (1) In spite of being supercritical, the core first contracts to a sheet perpendicular to the mean magnetic field, and the sheet itself collapses. (2) The solenoidal component of the turbulence remains at roughly its initial level throughout the simulation, while the compressible component increases continuously, implying that turbulence does not dissipate towards the centre of the core. (3) The distribution of simulation cells in the B–ρ plane occupies a wide triangular region at low densities, bounded below by the expected trend for fast MHD waves (B ∝ ρ, applicable for high-local Alfvénic Mach number MA) and above by the trend expected for slow waves (B ∼ constant, applicable for low local MA). At high densities, the distribution follows a single trend $$B \propto \rho ^{\gamma _{\rm eff}}$$, with 1/2 < γeff < 2/3, as expected for gravitational compression. (4) The mass-to-magnetic flux ratio λ increases with radius r due to the different scalings of the mass and magnetic flux with r. At a fixed radius, λ increases with time due to the accretion of material along field lines. (5) The solenoidal energy fraction is much smaller than the total turbulent component, indicating that the collapse drives the turbulence mainly compressibly, even in directions orthogonal to that of the collapse.
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- Award ID(s):
- 2307840
- PAR ID:
- 10504396
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 530
- Issue:
- 3
- ISSN:
- 0035-8711
- Format(s):
- Medium: X Size: p. 3431-3444
- Size(s):
- p. 3431-3444
- Sponsoring Org:
- National Science Foundation
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