On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence

TL;DR

This paper investigates how turbulence in a conducting fluid becomes two-dimensional under a magnetic field, using simulations to explain the dominance of horizontal energy contrary to linear predictions.

Contribution

It provides the first detailed nonlinear analysis of two-dimensionalization in quasistatic MHD turbulence through direct numerical simulations.

Findings

Turbulence evolves into a two-and-a-half-dimensional state.

Horizontal kinetic energy becomes dominant in the final state.

Nonlinear effects explain the deviation from linear decay predictions.

Abstract

We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [Moffatt, JFM 28, 1967]. However, numerous numerical studies predict a different behaviour, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using Direct Numerical Simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called "two-and-a-half-dimensional" flow [Montgomery & Turner, Phys. Fluids 25(2), 1982] and we offer an explanation for the dominance of horizontal kinetic energy.