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Bifurcations in narrow-gap spherical Couette flow

Published online by Cambridge University Press:  17 March 2025

Ananthu J.P. Open the ORCID record for Ananthu J.P. [Opens in a new window] ,
Manjul Sharma Open the ORCID record for Manjul Sharma [Opens in a new window] ,
A. Sameen Open the ORCID record for A. Sameen [Opens in a new window]  and
Vinod Narayanan Open the ORCID record for Vinod Narayanan [Opens in a new window]
Ananthu J.P.
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382355, India
Manjul Sharma
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
A. Sameen
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India Geophysical Flows Lab, Indian Institute of Technology Madras, Chennai 600036, India
Vinod Narayanan*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382355, India
*
Corresponding author: Vinod Narayanan, vinod@iitgn.ac.in
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Abstract

The incompressible Navier–Stokes equations in spherical coordinates are solved using a pseudo-spectral method to simulate the problem of spherical Couette flow. The flow is investigated for a narrow-gap ratio with only the inner sphere rotating. We find that the flow is sensitive to the initial conditions and have used various initial conditions to obtain different branches of the bifurcation curve of the flow. We have identified three different branches dominated respectively by axisymmetric flow, travelling wave instability and equatorial instability. The axisymmetric branch shows unsteadiness at large Reynolds numbers. The travelling wave instability branch shows spiral instability and is prominent the near poles. The travelling wave instability branch further exhibits a reversal in the propagation direction of the spiral instability as the Reynolds number is increased. This branch also exhibits a multi-mode equatorial instability at larger Reynolds numbers. The equatorial instability branch exhibits twin jet streams on either side of the equator, which become unstable at larger Reynolds numbers. The flow topology on the three branches is also investigated in their phase space and found to exhibit chaotic behaviour at large Reynolds numbers on the travelling wave instability branch.

JFM classification

Geophysical and Geological Flows: Rotating flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A64
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© The Author(s), 2025. Published by Cambridge University Press

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