## Abstract

We study two-dimensional magnetohydrodynamic turbulence, with an

emphasis on its energetics and inertial range scaling laws. A detailed

spectral analysis shows that dynamo triads (those converting kinetic

into magnetic energy) are associated with a direct magnetic energy

flux while anti-dynamo triads (those converting magnetic into kinetic

energy) are associated with an inverse magnetic energy flux. As both

dynamo and anti-dynamo interacting triads are integral parts of the

direct energy transfer, the anti-dynamo inverse flux partially

neutralizes the dynamo direct flux, arguably resulting in relatively

weak direct energy transfer and giving rise to dynamo saturation. This

result is consistent with a qualitative prediction of energy transfer

reduction owing to Alfv\'en wave effects by the Iroshnikov--Kraichnan

theory (which was originally formulated for magnetohydrodynamic

turbulence in three dimensions). We numerically confirm the correlation

between dynamo action and direct magnetic energy flux and investigate

the applicability of quantitative aspects of the Iroshnikov--Kraichnan

theory to the present case, particularly its predictions of energy

equipartition and $k^{-3/2}$ spectra in the energy inertial range.

It is found that for turbulence satisfying the Kraichnan condition

of magnetic energy at large scales exceeding total energy in the

inertial range, the kinetic energy spectrum, which is significantly

shallower than $k^{-3/2}$, is shallower than its magnetic counterpart.

This result suggests no energy equipartition. The total energy spectrum

appears to depend on the energy composition of the turbulence but is

clearly shallower than $k^{-3/2}$ for $r\approx2$, even at moderate

resolutions. Here $r\approx2$ is the magnetic-to-kinetic energy ratio

during the stage when the turbulence can be considered fully developed.

The implication of the present findings is discussed in conjunction with

further numerical results on the dependence of the energy dissipation

rate on resolution.

emphasis on its energetics and inertial range scaling laws. A detailed

spectral analysis shows that dynamo triads (those converting kinetic

into magnetic energy) are associated with a direct magnetic energy

flux while anti-dynamo triads (those converting magnetic into kinetic

energy) are associated with an inverse magnetic energy flux. As both

dynamo and anti-dynamo interacting triads are integral parts of the

direct energy transfer, the anti-dynamo inverse flux partially

neutralizes the dynamo direct flux, arguably resulting in relatively

weak direct energy transfer and giving rise to dynamo saturation. This

result is consistent with a qualitative prediction of energy transfer

reduction owing to Alfv\'en wave effects by the Iroshnikov--Kraichnan

theory (which was originally formulated for magnetohydrodynamic

turbulence in three dimensions). We numerically confirm the correlation

between dynamo action and direct magnetic energy flux and investigate

the applicability of quantitative aspects of the Iroshnikov--Kraichnan

theory to the present case, particularly its predictions of energy

equipartition and $k^{-3/2}$ spectra in the energy inertial range.

It is found that for turbulence satisfying the Kraichnan condition

of magnetic energy at large scales exceeding total energy in the

inertial range, the kinetic energy spectrum, which is significantly

shallower than $k^{-3/2}$, is shallower than its magnetic counterpart.

This result suggests no energy equipartition. The total energy spectrum

appears to depend on the energy composition of the turbulence but is

clearly shallower than $k^{-3/2}$ for $r\approx2$, even at moderate

resolutions. Here $r\approx2$ is the magnetic-to-kinetic energy ratio

during the stage when the turbulence can be considered fully developed.

The implication of the present findings is discussed in conjunction with

further numerical results on the dependence of the energy dissipation

rate on resolution.

Original language | English |
---|---|

Pages (from-to) | 238-254 |

Number of pages | 17 |

Journal | Journal of Fluid Mechanics |

Volume | 703 |

Early online date | 12 Jun 2012 |

DOIs | |

Publication status | Published - Jul 2012 |

## Keywords

- Magnetohydrodynamic Turbulence