Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics

David G. Dritschel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)525-541
Number of pages17
JournalJournal of Fluid Mechanics
Publication statusPublished - 1 Jan 1991


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