TY - JOUR
T1 - On General Transformations and Variational Principles for the Magnetohydrodynamics of Ideal Fluids. Part 1. Fundamental Principles
AU - Vladimirov, V. A.
PY - 1995/1
Y1 - 1995/1
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
AN - SCOPUS:0028992011
SN - 0022-1120
VL - 283
SP - 125
EP - 139
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -