Helical shell models for MHD

A shell model for magnetohydrodynamics (MHD) is derived directly from the dynamical system driving the evolution of three helical modes interacting in a triad. The use of helical modes implies that two shell variables are required for the velocity as well as for the magnetic field. The advantage of...

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Bibliographic Details
Published in:Theoretical and computational fluid dynamics 2009-11, Vol.23 (6), p.439-450
Main Authors: Lessinnes, T., Plunian, F., Carati, D.
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Computational Science and Engineering
Engineering
Engineering Fluid Dynamics
Fluid mechanics
Magnetic fields
Original Article
Turbulence models
Turbulent flow
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Summary:A shell model for magnetohydrodynamics (MHD) is derived directly from the dynamical system driving the evolution of three helical modes interacting in a triad. The use of helical modes implies that two shell variables are required for the velocity as well as for the magnetic field. The advantage of the method is the automatic conservation of all the ideal quadratic MHD invariants. The number of coupling constants is however larger than in traditional shell models. This difficulty is worked around by introducing an averaging procedure that allows to derive the shell model coupling constants directly from the MHD equations. The resulting shell model is used to explore the influence of a helical forcing on the global properties of MHD turbulence close to the onset of the dynamo regime.
ISSN:0935-4964
1432-2250
DOI:10.1007/s00162-009-0165-y