### 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 |

Publication status | Published - Apr 1997 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Plasmas*,

*4*(4), 1010-1017.

**New one-dimensional model equations of magnetohydrodynamic turbulence.** / Yanase, Shinichiro.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 4, no. 4, pp. 1010-1017.

}

TY - JOUR

T1 - New one-dimensional model equations of magnetohydrodynamic turbulence

AU - Yanase, Shinichiro

PY - 1997/4

Y1 - 1997/4

N2 - 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 by(x,t) and bz(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 by(x,t), bz(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.

AB - 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 by(x,t) and bz(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 by(x,t), bz(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.

UR - http://www.scopus.com/inward/record.url?scp=0031125809&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031125809&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031125809

VL - 4

SP - 1010

EP - 1017

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 4

ER -