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Bifurcation aspect of polygonal coherence over transitional Reynolds numbers in wide-gap spherical Couette flow

Fumitoshi Goto1, Tomoaki Itano2,*, Masako Sugihara-Seki2,3, and Takahiro Adachi4

  • 1Graduate School of Science and Engineering, Kansai University, Osaka 564-8680, Japan
  • 2Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University, Osaka, 564-8680, Japan
  • 3Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
  • 4Department of Systems Design Engineering, Akita University, Akita, 010-8502, Japan

  • *itano@kansai-u.ac.jp
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Phys. Rev. Fluids 6, 113903 – Published 22 November, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.113903

Abstract

This study numerically investigates the bifurcation aspect of the wide-gap spherical Couette flow (SCF), with an emphasis on the competition among polygonal coherence with different wave numbers observed over transitional Reynolds numbers. Focusing on a representative case, the half-radius ratio η=1/2, we confirm that the axisymmetric state becomes unstable over the first transitional Reynolds number at which the fourfold spiral state bifurcates, using the continuation method based on the Newton–Raphson algorithm. The Galerkin-spectral method was employed to numerically solve the governing equations. It is found that the threefold spiral state bifurcates from the axisymmetric state at a slightly higher Reynolds number than the first transitional Reynolds number. The attraction of the threefold spiral state expands rapidly with an increase in the Reynolds number, which is determined by verifying the distance of the unstable periodiclike state to both spiral states in the state space. This aspect of the state space explains the experimentally bistable realization of different equilibrium states over the first transitional Reynolds number. This study also found that the periodiclike state is composed of the three- and fourfold spiral states, similar to a beat with two different frequencies.

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Outline

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Phys. Rev. Fluids 6, 113903– Published 22 November, 2021
  • Received 17 August 2021
  • Accepted 5 November 2021
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