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The European Physical Journal B

, Volume 60, Issue 3, pp 337–351 | Cite as

Eddy diffusivity in convective hydromagnetic systems

Physics of Fluids

Abstract.

An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries, kept at fixed temperatures and with free surface boundary conditions for the velocity field; periodicity in horizontal directions is assumed. The steady states must be stable to short (fast) scale perturbations and possess symmetry about the vertical axis, allowing instabilities involving large (slow) scales to develop. We expand the modes and their growth rates in power series in the scale separation parameter and obtain a hierarchy of equations, which are solved numerically. Second order solvability condition yields a closed equation for the leading terms of the asymptotic expansions and respective growth rate, whose origin is in the (combined) eddy diffusivity phenomenon. For about 10% of randomly generated steady convective hydromagnetic regimes, negative eddy diffusivity is found.

PACS.

47.65.-d Magnetohydrodynamics and electrohydrodynamics 47.10.-g General theory in fluid dynamics 47.27.-i Turbulent flows 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • M. Baptista
    • 1
  • S. M.A. Gama
    • 1
  • V. A. Zheligovsky
    • 2
    • 3
    • 4
  1. 1.Centro de Matemática da Universidade do Porto and Departamento de Matemática Aplicada, Faculdade de Ciências da Universidade do PortoPortoPortugal
  2. 2.International Institute of Earthquake Prediction Theory and Mathematical GeophysicsMoscowRussian Federation
  3. 3.Institute of Mechanics, Lomonosov Moscow State University 1MoscowRussian Federation
  4. 4.Observatoire de la Côte d'Azur, CNRS U.M.R. 6529Nice Cedex 4France

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