### Abstract

New one-dimensional model equations of magnetohydrodynamic turbulence depending on the position x and the time t are proposed considering the x component of the velocity u(x,t) and the y and z components of the magnetic field b_{y}(x,t) and b_{z}(x,t). It is found that the model equations conserve the total energy and the quantity similar to the cross helicity, and that they have a similarity solution, u(x,t)∼x/t and b_{y}(x,t), b_{z}(x,t)∼C/t in the inviscid limit. A shock type solution is obtained where both the velocity and the magnetic fields have a jump in a narrow viscous or diffusive region. Numerical simulations are also carried out and the results show that the k^{-2} energy spectrum develops both for the velocity and the magnetic fields.

Original language | English |
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Pages (from-to) | 1010-1017 |

Number of pages | 8 |

Journal | Physics of Plasmas |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1997 |

### ASJC Scopus subject areas

- Condensed Matter Physics