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

TL;DR

This paper introduces symmetry-preserving initial conditions for magnetohydrodynamics, enabling high-resolution simulations up to 2048^3 grid points, and analyzes the ideal flow behavior and current sheet collisions.

Contribution

It presents new symmetric initial conditions for MHD that reduce computational costs and explores the ideal flow dynamics and current sheet interactions at unprecedented resolutions.

Findings

Exponential decay of energy spectrum persists at high resolution.

Flow remains regular with no singularity formation during decay.

Collision of current sheets causes rapid magnetic field rotation and strong gradients.

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.