A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets

Abstract

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal non-dissipative case is studied up to the equivalent of 2048^3 grid points for one of these flows. The temporal evolution of the logarithmic decrements, delta, of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.

8 pages, 4 figures

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Cited by in corpus (11)

• On the lack of universality in decaying magnetohydrodynamic turbulence
• Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem
• Axial dipolar dynamo action in the Taylor-Green vortex
• Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence
• Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
• The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD
• A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics
• Turbulent cascade, bottleneck and thermalized spectrum in hyperviscous flows
• The origins of $k^{-2}$ spectrum in the decaying Taylor-Green magnetohydrodynamic turbulent flows
• Self-truncation and scaling in Euler-Voigt-$\alpha$ and related fluid models
• Magnetized Decaying Turbulence in the Weakly Compressible Taylor-Green Vortex