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Title: Reduced Lorenz models for anomalous transport and profile resilience

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.

Authors:
;  [1];  [2]
  1. Department of Physics and Technology, University of Tromsoe, N-9037 Tromsoe (Norway)
  2. (Denmark)
Publication Date:
OSTI Identifier:
20974817
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2435318; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; DIFFUSION; EQUATIONS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLASMA

Citation Formats

Rypdal, K., Garcia, O. E., and Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde. Reduced Lorenz models for anomalous transport and profile resilience. United States: N. p., 2007. Web. doi:10.1063/1.2435318.
Rypdal, K., Garcia, O. E., & Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde. Reduced Lorenz models for anomalous transport and profile resilience. United States. doi:10.1063/1.2435318.
Rypdal, K., Garcia, O. E., and Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde. Thu . "Reduced Lorenz models for anomalous transport and profile resilience". United States. doi:10.1063/1.2435318.
@article{osti_20974817,
title = {Reduced Lorenz models for anomalous transport and profile resilience},
author = {Rypdal, K. and Garcia, O. E. and Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde},
abstractNote = {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.},
doi = {10.1063/1.2435318},
journal = {Physics of Plasmas},
number = 2,
volume = 14,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}