### Abstract

The energy method was used to investigate the stability of steady magnetohydrodynamic flows in an inviscid incompressible fluid. It was found that if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations were also stable. Sufficient conditioons for linear stability were obtained from these results. Thus, it was shown that certain classes of steady magnetohydrodynamic flows, in which both the magnetic field and the velocity depend on all the three spatial coordinates, are stable.

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

Pages (from-to) | 3586-3594 |

Number of pages | 9 |

Journal | Physics of Plasmas |

Volume | 11 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2004 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Plasmas*,

*11*(7), 3586-3594. https://doi.org/10.1063/1.1759337

**Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation.** / Ilin, K. I.; Vladimirov, V. A.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 11, no. 7, pp. 3586-3594. https://doi.org/10.1063/1.1759337

}

TY - JOUR

T1 - Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

AU - Ilin, K. I.

AU - Vladimirov, V. A.

PY - 2004/7

Y1 - 2004/7

N2 - The energy method was used to investigate the stability of steady magnetohydrodynamic flows in an inviscid incompressible fluid. It was found that if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations were also stable. Sufficient conditioons for linear stability were obtained from these results. Thus, it was shown that certain classes of steady magnetohydrodynamic flows, in which both the magnetic field and the velocity depend on all the three spatial coordinates, are stable.

AB - The energy method was used to investigate the stability of steady magnetohydrodynamic flows in an inviscid incompressible fluid. It was found that if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations were also stable. Sufficient conditioons for linear stability were obtained from these results. Thus, it was shown that certain classes of steady magnetohydrodynamic flows, in which both the magnetic field and the velocity depend on all the three spatial coordinates, are stable.

UR - http://www.scopus.com/inward/record.url?scp=3142692532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142692532&partnerID=8YFLogxK

U2 - 10.1063/1.1759337

DO - 10.1063/1.1759337

M3 - Article

VL - 11

SP - 3586

EP - 3594

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 7

ER -