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Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics

Published online by Cambridge University Press:  26 April 2006

David G. Dritschel
David G. Dritschel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

The nonlinear, three-dimensional Euler equations can be reduced to a simple linear equation when the flow has helical symmetry and when the flow consists of a rigidly rotating basic part plus a Beltrami disturbance part (with vorticity proportional to velocity or a slight generalization of this). Solutions to this linear equation represent steadily rotating, non-axisymmetric waves of arbitrary amplitude. Exact solutions can be constructed in the case of flow in a straight pipe of circular cross-section. Analogous results are obtained for the incompressible, non-dissipative equations of magnetohydrodynamics. In addition to a rigidly rotating basic flow, there may exist a toroidal magnetic field varying linearly with radius.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 525 - 541
Copyright
© 1991 Cambridge University Press

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