Bifurcation and phase diagram of turbulence constituted from three different scale-length modes

S. I. Itoh, A. Kitazawa, M. Yagi, K. Itoh

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Cases where three kinds of fluctuations having the different typical scale lengths coexist are analysed, and the Statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analysed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analysed and a phase diagram is drawn. Phase diagrams with cusp-type catastrophe and butterfly-type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analysed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses.

Original languageEnglish
Pages (from-to)1311-1328
Number of pages18
JournalPlasma Physics and Controlled Fusion
Volume44
Issue number7
DOIs
Publication statusPublished - Jul 1 2002

Fingerprint

Phase diagrams
Turbulence
turbulence
diagrams
phase diagrams
Beam plasma interactions
Drag
Quenching
Plasmas
cusps
drag
quenching
shift
interactions

All Science Journal Classification (ASJC) codes

  • Nuclear Energy and Engineering
  • Condensed Matter Physics

Cite this

Bifurcation and phase diagram of turbulence constituted from three different scale-length modes. / Itoh, S. I.; Kitazawa, A.; Yagi, M.; Itoh, K.

In: Plasma Physics and Controlled Fusion, Vol. 44, No. 7, 01.07.2002, p. 1311-1328.

Research output: Contribution to journalArticle

Itoh, S. I. ; Kitazawa, A. ; Yagi, M. ; Itoh, K. / Bifurcation and phase diagram of turbulence constituted from three different scale-length modes. In: Plasma Physics and Controlled Fusion. 2002 ; Vol. 44, No. 7. pp. 1311-1328.
@article{e9e041aea0da4bdf8011788f6773281c,
title = "Bifurcation and phase diagram of turbulence constituted from three different scale-length modes",
abstract = "Cases where three kinds of fluctuations having the different typical scale lengths coexist are analysed, and the Statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analysed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analysed and a phase diagram is drawn. Phase diagrams with cusp-type catastrophe and butterfly-type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analysed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses.",
author = "Itoh, {S. I.} and A. Kitazawa and M. Yagi and K. Itoh",
year = "2002",
month = "7",
day = "1",
doi = "10.1088/0741-3335/44/7/319",
language = "English",
volume = "44",
pages = "1311--1328",
journal = "Plasma Physics and Controlled Fusion",
issn = "0741-3335",
publisher = "IOP Publishing Ltd.",
number = "7",

}

TY - JOUR

T1 - Bifurcation and phase diagram of turbulence constituted from three different scale-length modes

AU - Itoh, S. I.

AU - Kitazawa, A.

AU - Yagi, M.

AU - Itoh, K.

PY - 2002/7/1

Y1 - 2002/7/1

N2 - Cases where three kinds of fluctuations having the different typical scale lengths coexist are analysed, and the Statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analysed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analysed and a phase diagram is drawn. Phase diagrams with cusp-type catastrophe and butterfly-type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analysed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses.

AB - Cases where three kinds of fluctuations having the different typical scale lengths coexist are analysed, and the Statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analysed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analysed and a phase diagram is drawn. Phase diagrams with cusp-type catastrophe and butterfly-type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analysed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses.

UR - http://www.scopus.com/inward/record.url?scp=0036648385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036648385&partnerID=8YFLogxK

U2 - 10.1088/0741-3335/44/7/319

DO - 10.1088/0741-3335/44/7/319

M3 - Article

AN - SCOPUS:0036648385

VL - 44

SP - 1311

EP - 1328

JO - Plasma Physics and Controlled Fusion

JF - Plasma Physics and Controlled Fusion

SN - 0741-3335

IS - 7

ER -