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Instabilities of the Stewartson layer Part 2. Supercritical mode transitions

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Abstract

We investigate, both experimentally and numerically, the fluid flow in a spherical shell with radius ratio ri/ro=2/3. Both spheres rotate about a common axis, with Ωi>Ωo. The basic state consists of a Stewartson layer situated on the tangent cylinder, the cylinder parallel to the axis of rotation and touching the inner sphere. If the differential rotation is sufficiently large, non-axisymmetric instabilities arise, with the wavenumber of the most unstable mode increasing with increasing overall rotation. In the increasingly supercritical regime, a series of mode transitions occurs in which the wavenumber decreases again. The experimental and numerical results are in good agreement regarding this basic sequence of mode transitions, and the numerics are then used to study some of the finer details of the solutions that could not be observed in the experiment.

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Authors and Affiliations

  1. Department of Aerodynamics and Fluid Mechanics, Brandenburg Technical University, 03013, Cottbus, Germany

    Rainer Hollerbach, Birgit Futterer, Tamar More & Christoph Egbers

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  1. Rainer Hollerbach
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  2. Birgit Futterer
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  3. Tamar More
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  4. Christoph Egbers
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Correspondence to Rainer Hollerbach.

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Communicated by

H.J.S. Fernando

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Hollerbach, R., Futterer, B., More, T. et al. Instabilities of the Stewartson layer Part 2. Supercritical mode transitions. Theor. Comput. Fluid Dyn. 18, 197–204 (2004). https://doi.org/10.1007/s00162-004-0125-5

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  • DOI: https://doi.org/10.1007/s00162-004-0125-5

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