Nondissipative Magneto-Hydrodynamic Flows with Magnetic and Velocity Field Lines Orthogonal Geodesics

By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of nondissipative magneto-hydrodynamic flows. For the latter, the velocity and magnetic field lines are geodesics and parallels respectively on a normal congruence of surfaces. A si...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1974-01, Vol.26 (1), p.183-195
Main Authors: Rogers, Colin, Kingston, John G.
Format: Article
Language:English
Subjects:
Boundary conditions
Coordinate systems
Curvature
Decomposition
Flow velocity
Fluid mechanics
Geodesic lines
Magnetic fields
Magnetism
Mathematical congruence
Orthogonal lines
Partial differential equations
Sine function
Vector fields
Velocity
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Summary:By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of nondissipative magneto-hydrodynamic flows. For the latter, the velocity and magnetic field lines are geodesics and parallels respectively on a normal congruence of surfaces. A significant subclass is shown to be helical in character.
ISSN:0036-1399
1095-712X
DOI:10.1137/0126015