Magnetohydrodynamic drift equations

From Langmuir circulations to magnetohydrodynamic dynamo?

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume698
DOIs
Publication statusPublished - May 10 2012

Fingerprint

Magnetohydrodynamics
magnetohydrodynamics
Magnetic fields
Oscillating flow
Electric commutators
Advection
Vortex flow
Earth (planet)
oscillating flow
commutators
Reynolds stress
advection
magnetic fields
velocity distribution
time measurement
vortices

Keywords

  • dynamo theory
  • general fluid mechanics
  • magnetohydrodynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Magnetohydrodynamic drift equations : From Langmuir circulations to magnetohydrodynamic dynamo? / Vladimirov, V. A.

In: Journal of Fluid Mechanics, Vol. 698, 10.05.2012, p. 51-61.

Research output: Contribution to journalArticle

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