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Title: Temporal chaos in Boussinesq magnetoconvection

Abstract

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famous Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.

Authors:
;  [1];  [2]
  1. College of Engineering, Nihon University, Koriyama, Fukushima 963-8642 (Japan)
  2. (Japan)
Publication Date:
OSTI Identifier:
20960094
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2430517; (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; BIFURCATION; BOUNDARY CONDITIONS; CONVECTION; ELECTRON TEMPERATURE; FLUCTUATIONS; FLUIDS; ION TEMPERATURE; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PARTIAL DIFFERENTIAL EQUATIONS; PLASMA; PLASMA SIMULATION; STRESSES; TURBULENCE; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Bekki, Naoaki, Moriguchi, Hirofumi, and Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495. Temporal chaos in Boussinesq magnetoconvection. United States: N. p., 2007. Web. doi:10.1063/1.2430517.
Bekki, Naoaki, Moriguchi, Hirofumi, & Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495. Temporal chaos in Boussinesq magnetoconvection. United States. doi:10.1063/1.2430517.
Bekki, Naoaki, Moriguchi, Hirofumi, and Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495. Mon . "Temporal chaos in Boussinesq magnetoconvection". United States. doi:10.1063/1.2430517.
@article{osti_20960094,
title = {Temporal chaos in Boussinesq magnetoconvection},
author = {Bekki, Naoaki and Moriguchi, Hirofumi and Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495},
abstractNote = {Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famous Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.},
doi = {10.1063/1.2430517},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
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  • Two numerical techniques are proposed to construct a polynomial chaos (PC) representation of an arbitrary second-order random vector. In the first approach, a PC representation is constructed by matching a target joint probability density function (pdf) based on sequential conditioning (a sequence of conditional probability relations) in conjunction with the Rosenblatt transformation. In the second approach, the PC representation is obtained by having recourse to the Rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target Spearman's rank correlation coefficient (SRCC) matrix. Both techniques are applied to model an experimental spatio-temporal data set, exhibiting strong non-stationary andmore » non-Gaussian features. The data consists of a set of oceanographic temperature records obtained from a shallow-water acoustics transmission experiment. The measurement data, observed over a finite denumerable subset of the indexing set of the random process, is treated as a collection of observed samples of a second-order random vector that can be treated as a finite-dimensional approximation of the original random field. A set of properly ordered conditional pdfs, that uniquely characterizes the target joint pdf, in the first approach and a set of target marginal pdfs and a target SRCC matrix, in the second approach, are estimated from available experimental data. Digital realizations sampled from the constructed PC representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy. The relative advantages and disadvantages of the two proposed techniques are also highlighted.« less
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  • A two-dimensional Boussinesq fluid with nonlinear interaction between Rayleigh--Benard convection and an external magnetic field is investigated numerically and analytically. A simplified model consisting of a fifth-order system of nonlinear ordinary differential equations with five parameters is introduced and integrated numerically in certain parameter regions. Various types of bifurcations from periodic solutions are found numerically: period-doubling bifurcation, heteroclinic bifurcation, intermittency, and saddle-node bifurcation. A normal form equation is also derived from the fifth-order system, and center manifold theory is applied to it. An expression for the renormalized Holmes--Melnikov boundary for the evaluation of the numerical results is given. It ismore » shown from the normal form equation that each property of the two phase portraits described by the Duffing equation and the van der Pol equation emanates from one common attractor in the five-dimensional space of the fifth-order system. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • In a recent paper, N. Bekki and T. Karakisawa (Ref. 1) considered two-dimensional Boussinesq convection in an imposed vertical magnetic field. We would like to point out that a number of their results and claims are incorrect. These can be seen by comparing their work with ours. (AIP). {copyright}{ital 1996 American Institute of Physics}