### Abstract

A new frozen-in field w (generalizing vorticity) is constructed for ideal magnetohydrodynamic flow. In conjunction with the frozen-in magnetic field h, this is used to obtain a generalized Weber transformation of the MHD equations, expressing the velocity as a bilinear form in generalized Weber variables. This expression is also obtained from Hamilton’s principle of least action, and the canonically conjugate Hamiltonian variables for MHD flow are identified. Two alternative energy-type variational principles for three-dimensional steady MHD flow are established. Both involve a functional R which is the sum of the total energy and another conserved functional, the volume integral of a function ϕ of Lagrangian coordinates. It is shown that the first variation δ^{1}R vanishes if ϕ is suitably chosen (as minus a generalized Bernoulli integral). Expressions for the second variation δ^{2}R are presented.

Original language | English |
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Pages (from-to) | 125-139 |

Number of pages | 15 |

Journal | Journal of Fluid Mechanics |

Volume | 283 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

**On General Transformations and Variational Principles for the Magnetohydrodynamics of Ideal Fluids. Part 1. Fundamental Principles.** / Vladimirov, V. A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On General Transformations and Variational Principles for the Magnetohydrodynamics of Ideal Fluids. Part 1. Fundamental Principles

AU - Vladimirov, V. A.

PY - 1995

Y1 - 1995

N2 - A new frozen-in field w (generalizing vorticity) is constructed for ideal magnetohydrodynamic flow. In conjunction with the frozen-in magnetic field h, this is used to obtain a generalized Weber transformation of the MHD equations, expressing the velocity as a bilinear form in generalized Weber variables. This expression is also obtained from Hamilton’s principle of least action, and the canonically conjugate Hamiltonian variables for MHD flow are identified. Two alternative energy-type variational principles for three-dimensional steady MHD flow are established. Both involve a functional R which is the sum of the total energy and another conserved functional, the volume integral of a function ϕ of Lagrangian coordinates. It is shown that the first variation δ1R vanishes if ϕ is suitably chosen (as minus a generalized Bernoulli integral). Expressions for the second variation δ2R are presented.

AB - A new frozen-in field w (generalizing vorticity) is constructed for ideal magnetohydrodynamic flow. In conjunction with the frozen-in magnetic field h, this is used to obtain a generalized Weber transformation of the MHD equations, expressing the velocity as a bilinear form in generalized Weber variables. This expression is also obtained from Hamilton’s principle of least action, and the canonically conjugate Hamiltonian variables for MHD flow are identified. Two alternative energy-type variational principles for three-dimensional steady MHD flow are established. Both involve a functional R which is the sum of the total energy and another conserved functional, the volume integral of a function ϕ of Lagrangian coordinates. It is shown that the first variation δ1R vanishes if ϕ is suitably chosen (as minus a generalized Bernoulli integral). Expressions for the second variation δ2R are presented.

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U2 - 10.1017/S0022112095002254

DO - 10.1017/S0022112095002254

M3 - Article

VL - 283

SP - 125

EP - 139

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -