Tertiary and Quaternary States in the Taylor-Couette System

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

doi:10.1016/j.chaos.2018.01.033

Tertiary and Quaternary States in the Taylor-Couette System

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

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	107-117
Journal	Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena
Volume	109
Early online date	23 Feb 2018
DOIs	https://doi.org/10.1016/j.chaos.2018.01.033
Publication status	Published - 1 Apr 2018

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

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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.",

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AU - Busse, F.h.

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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

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JO - Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena

JF - Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena

ER -

Tertiary and Quaternary States in the Taylor-Couette System

Abstract

Bibliographical note

Keywords

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