Magnetohydrodynamic drift equations: From Langmuir circulations to magnetohydrodynamic dynamo?

V. A. Vladimirov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We derive the closed system of averaged magnetohydrodynamic (MHD) equations for general oscillating flows. The used small parameter of our asymptotic theory is the dimensionless inverse frequency, and the leading term for a velocity field is chosen to be purely oscillating. The employed mathematical approach combines the two-timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equations are similar to the original MHD equations, but surprisingly (instead of the commonly expected Reynolds stresses) a drift velocity plays a part of an additional advection velocity. In the special case of a vanishing magnetic field h=0, the averaged equations produce the Craik-Leibovich equations for Langmuir circulations (which can be called 'vortex dynamo'). We suggest that, since the mathematical structure of the full averaged equations for h ≠ 0 is similar to those for h = 0, these full equations could lead to a possible mechanism of MHD dynamo, such as the generation of the magnetic field of the Earth.

Original languageEnglish
Pages (from-to)51-61
Number of pages11
JournalJournal of Fluid Mechanics
Publication statusPublished - May 10 2012


  • dynamo theory
  • general fluid mechanics
  • magnetohydrodynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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