Tertiary and Quaternary States in the Taylor-Couette System

Akinaga, T., Generalis, S.c. and 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 , pp. 107-117.

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.

Publication DOI: https://doi.org/10.1016/j.chaos.2018.01.033
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: © 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)
Uncontrolled Keywords: Bifurcation theory,nonlinearity,Floquet parameters, stability
Full Text Link: http://linkinghub.elsevier.com/retrieve/pii/S096007791830033X
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Published Date: 2018-04-01
Authors: Akinaga, T. ( 0000-0001-7402-5436)
Generalis, S.c. ( 0000-0001-7660-0633)
Busse, F.h.

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