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Flow-history effect on higher modes in the spherical Couette system

Published online by Cambridge University Press:  26 April 2006

Koichi Nakabayashi  and
Yoichi Tsuchida
Koichi Nakabayashi
Affiliation:
Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466, Japan
Yoichi Tsuchida
Affiliation:
Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466, Japan
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Abstract

Our flow-visualization and spectral studies of spherical Couette flow between two concentric spheres with only the inner sphere rotating for the clearance ratio (or gap ratio) 0.14 where the Taylor instability occurs have been pursued to systematically explore how and why a variety of wavenumbers and rotation frequencies of the non-axisymmetric periodic disturbances occurs at the same supercritical Reynolds number. The observed periodic disturbances constitute six kinds of disturbances: spiral TG (Taylor–Görtler) vortices, twists developing within toroidal TG vortices, both unmodulated and modulated waves travelling on the TG vortices, and both Stuart vortices and shear waves developing within the Ekman-type secondary flow. Development of these disturbances depends strongly on the flow mode at the initial Reynolds number (initial flow mode) and on the Reynolds-number evolution process approaching the final Reynolds number (acceleration rate and history of the Reynolds number). In our previous studies (Nakabayashi 1983; Nakabayashi & Tsuchida 1988 a, b), we clarified the structures, wavenumbers and rotation frequencies of the periodic disturbances caused by a quasi-static increasing of the Reynolds number. In the present study, we consider how the characteristics of periodic disturbances depend on the following three factors: (i) the rate of increase of the Reynolds number; (ii) the number of toroidal vortices in an initial flow mode; and (iii) the quasi-static Reynolds-number history. The flow modes observed in the present study are all stable to small perturbations, and the transitions among the flow modes are reproducible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 43 - 60
Copyright
© 1995 Cambridge University Press

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