Reduced Lorenz models for anomalous transport and profile resilience

K. Rypdal, Odd Erik Garcia

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    Abstract

    The physical basis for the Lorenz equations for convective cells in stratified fluids, and for magnetized plasmas imbedded in curved magnetic fields, are reexamined with emphasis on anomalous transport. It is shown that the Galerkin truncation leading to the Lorenz equations for the closed boundary problem is incompatible with finite fluxes through the system in the limit of vanishing diffusion. An alternative formulation leading to the Lorenz equations is proposed, invoking open boundaries and the notion of convective streamers and their back-reaction on the profile gradient, giving rise to resilience of the profile. Particular emphasis is put on the diffusionless limit, where these equations reduce to a simple dynamical system depending only on one single forcing parameter. This model is studied numerically, stressing experimentally observable signatures, and some of the perils of dimension-reducing approximations are discussed.(c) 2007 American Institute of Physics.
    Original languageEnglish
    JournalPhysics of Plasmas
    Volume14
    Issue number2
    Pages (from-to)022101
    ISSN1070-664X
    DOIs
    Publication statusPublished - 2007

    Bibliographical note

    Copyright (2007) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

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