Tertiary and Quaternary States in the Taylor-Couette System

T. Akinaga, S.c. Generalis, F.h. Busse

Research output: Contribution to journalArticle

Abstract

The analysis of the Taylor-Couette problem in the small gap limit is extended to the cases of tertiary and quaternary solutions. The theoretical results are compared with experimental observations. Although in the latter the small-gap approximation is not always well approximated, the comparison of theoretical results and observations yields reasonable agreements. The absence of the wavy twist mode in the observed patterns is explained by the presence of no-slip boundary conditions in the axial direction of the experimental apparatus, which differ from the periodic conditions imposed in the theoretical analysis. Quaternary solutions bifurcating from the tertiary ones through subharmonic instabilities are presented and compared with experimental observations. Reasonable agreement has been found.
Original languageEnglish
Pages (from-to)107-117
JournalChaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena
Volume109
Early online date23 Feb 2018
DOIs
Publication statusPublished - 1 Apr 2018

Fingerprint

Slip Boundary Condition
Subharmonics
Boundary conditions
Twist
Theoretical Analysis
slip
boundary conditions
Approximation
approximation
Observation

Bibliographical note

© 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Funding: Marie Curie IIF (Grant no. 298891) from the European Union and by the Leverhulme Trust (Grant no. VP1-2012-017)

Keywords

  • Bifurcation theory
  • nonlinearity
  • Floquet parameters
  • stability

Cite this

Akinaga, T., Generalis, S. C., & Busse, F. H. (2018). Tertiary and Quaternary States in the Taylor-Couette System. Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena, 109, 107-117. https://doi.org/10.1016/j.chaos.2018.01.033
Akinaga, T. ; Generalis, S.c. ; Busse, F.h. / Tertiary and Quaternary States in the Taylor-Couette System. In: Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena. 2018 ; Vol. 109. pp. 107-117.
@article{2a10878b18c847a1b53b0f76dec343b5,
title = "Tertiary and Quaternary States in the Taylor-Couette System",
abstract = "The analysis of the Taylor-Couette problem in the small gap limit is extended to the cases of tertiary and quaternary solutions. The theoretical results are compared with experimental observations. Although in the latter the small-gap approximation is not always well approximated, the comparison of theoretical results and observations yields reasonable agreements. The absence of the wavy twist mode in the observed patterns is explained by the presence of no-slip boundary conditions in the axial direction of the experimental apparatus, which differ from the periodic conditions imposed in the theoretical analysis. Quaternary solutions bifurcating from the tertiary ones through subharmonic instabilities are presented and compared with experimental observations. Reasonable agreement has been found.",
keywords = "Bifurcation theory, nonlinearity, Floquet parameters, stability",
author = "T. Akinaga and S.c. Generalis and F.h. Busse",
note = "{\circledC} 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Funding: Marie Curie IIF (Grant no. 298891) from the European Union and by the Leverhulme Trust (Grant no. VP1-2012-017)",
year = "2018",
month = "4",
day = "1",
doi = "10.1016/j.chaos.2018.01.033",
language = "English",
volume = "109",
pages = "107--117",

}

Akinaga, T, Generalis, SC & Busse, FH 2018, 'Tertiary and Quaternary States in the Taylor-Couette System', Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena, vol. 109, pp. 107-117. https://doi.org/10.1016/j.chaos.2018.01.033

Tertiary and Quaternary States in the Taylor-Couette System. / Akinaga, T.; Generalis, S.c.; Busse, F.h.

In: Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena, Vol. 109, 01.04.2018, p. 107-117.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Tertiary and Quaternary States in the Taylor-Couette System

AU - Akinaga, T.

AU - Generalis, S.c.

AU - Busse, F.h.

N1 - © 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Funding: Marie Curie IIF (Grant no. 298891) from the European Union and by the Leverhulme Trust (Grant no. VP1-2012-017)

PY - 2018/4/1

Y1 - 2018/4/1

N2 - The analysis of the Taylor-Couette problem in the small gap limit is extended to the cases of tertiary and quaternary solutions. The theoretical results are compared with experimental observations. Although in the latter the small-gap approximation is not always well approximated, the comparison of theoretical results and observations yields reasonable agreements. The absence of the wavy twist mode in the observed patterns is explained by the presence of no-slip boundary conditions in the axial direction of the experimental apparatus, which differ from the periodic conditions imposed in the theoretical analysis. Quaternary solutions bifurcating from the tertiary ones through subharmonic instabilities are presented and compared with experimental observations. Reasonable agreement has been found.

AB - The analysis of the Taylor-Couette problem in the small gap limit is extended to the cases of tertiary and quaternary solutions. The theoretical results are compared with experimental observations. Although in the latter the small-gap approximation is not always well approximated, the comparison of theoretical results and observations yields reasonable agreements. The absence of the wavy twist mode in the observed patterns is explained by the presence of no-slip boundary conditions in the axial direction of the experimental apparatus, which differ from the periodic conditions imposed in the theoretical analysis. Quaternary solutions bifurcating from the tertiary ones through subharmonic instabilities are presented and compared with experimental observations. Reasonable agreement has been found.

KW - Bifurcation theory

KW - nonlinearity

KW - Floquet parameters

KW - stability

U2 - 10.1016/j.chaos.2018.01.033

DO - 10.1016/j.chaos.2018.01.033

M3 - Article

VL - 109

SP - 107

EP - 117

ER -

Akinaga T, Generalis SC, Busse FH. Tertiary and Quaternary States in the Taylor-Couette System. Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena. 2018 Apr 1;109:107-117. https://doi.org/10.1016/j.chaos.2018.01.033