Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

K.I. Ilin; Vladimir Vladimirov

doi:10.1063/1.1759337

Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

K.I. Ilin, Vladimir Vladimirov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: 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 are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.

Original language	English
Pages (from-to)	3586-3594
Number of pages	8
Journal	Physics of Plasmas
Volume	11
Issue number	7
DOIs	https://doi.org/10.1063/1.1759337
Publication status	Published - Jul 2004

Keywords

plasma magnetohydrodynamics,
plasma instability

Access to Document

10.1063/1.1759337

http://dx.doi.org/10.1063/1.1759337

Cite this

@article{a4cce790efe7493999f203364a63de68,

title = "Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation",

abstract = "The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: 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 are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.",

keywords = "plasma magnetohydrodynamics, , plasma instability ",

author = "K.I. Ilin and Vladimir Vladimirov",

year = "2004",

month = jul,

doi = "10.1063/1.1759337",

language = "English",

volume = "11",

pages = "3586--3594",

journal = "Physics of Plasmas",

issn = "1070-664X",

publisher = "American Institute of Physics",

number = "7",

}

TY - JOUR

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

AU - Ilin, K.I.

AU - Vladimirov, Vladimir

PY - 2004/7

Y1 - 2004/7

N2 - The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: 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 are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.

AB - The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: 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 are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.

KW - plasma magnetohydrodynamics,

KW - plasma instability

U2 - 10.1063/1.1759337

DO - 10.1063/1.1759337

M3 - Article

SN - 1070-664X

VL - 11

SP - 3586

EP - 3594

JO - Physics of Plasmas

JF - Physics of Plasmas

IS - 7

ER -