Acta Mechanica

, Volume 230, Issue 10, pp 3499–3509 | Cite as

Numerical study on the axisymmetric state in spherical Couette flow under unstable thermal stratification

  • Taishi Inagaki
  • Tomoaki ItanoEmail author
  • Masako Sugihara-Seki
Original Paper


This paper numerically investigates the shear flow between double concentric spherical boundaries rotating differentially, the so-called spherical Couette flow, under unstable thermal stratification, focusing on the boundary of the axisymmetric/nonaxisymmetric transition in wide-gap cases where the inner radius is comparable to the clearance width. While the transition of SCF has been confirmed experimentally in cases without thermal factor, insufficient knowledge on SCF subject to thermal instability, related to geophysical problems especially in the wide-gap cases, has been accumulated mainly based on numerical analysis; our motivation is to bridge the knowledge gap by a parameter extension. We reconfirm that the transition under no thermal effect is initiated by a disturbance visualised as a spiral pattern with n arms extending from the equatorial zone to the pole in each hemisphere, at the critical Reynolds number, \({{{Re}}}_{\mathrm{cr}}\), as previously reported. With increasing thermal factor, the buoyancy effect enables the system rotation to trigger a transition towards nonaxisymmetric states, resulting in a relative decrease in \({{{Re}}}_{\mathrm{cr}}\). This is in contrast with the result that the system rotation apparently suppresses via Coriolis effect the transition to the thermally convective states at low Reynolds numbers. The present study elucidates that the existence of the axisymmetric state is restricted within a closed area in the extended parameter space, along the boundary of which the spiral patterns observed experimentally in SCF continuously connect to the classical spherical Bénard convective states.



We thank Prof. Kageyama, Dr. Hori, Dr. Yokoyama, Prof. J. Seki, and Prof. N. Sugimoto for their critical comments at the earlier stages of the study. T.I. expresses cordial thanks to Prof. Adachi for offering his numerical code based on the spectral element method to check the validity of our code. T.I. is grateful for partial financial support from the Kansai University Subsidy for Supporting Young Scholars, 2016–2017, and an ORDIST group fund, 2018. M.S. is grateful for partial financial support from KAKENHI 17H03176. Finally, we would like to thank Editage for English language editing.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Pure and Applied Physics, Faculty of Engineering ScienceKansai UniversityOsakaJapan

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