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Destabilization of free convection by weak rotation

Published online by Cambridge University Press:  21 September 2011

A. Yu. Gelfgat
A. Yu. Gelfgat*
Affiliation:
School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, 69978, Tel-Aviv, Israel
*
†Email address for correspondence: [email protected]
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Abstract

This study offers an explanation of the recently observed effect of destabilization of free convective flows by weak rotation. After studying several models where flows are driven by the simultaneous action of convection and rotation, it is concluded that destabilization is observed in cases where the centrifugal force acts against the main convective circulation. At relatively low Prandtl numbers, this counter-action can split the main vortex into two counter-rotating vortices, where the interaction leads to instability. At larger Prandtl numbers, the counter-action of the centrifugal force steepens an unstable thermal stratification, which triggers the Rayleigh–Bénard instability mechanism. Both cases can be enhanced by advection of azimuthal velocity disturbances towards the axis, where they grow and excite perturbations of the radial velocity. The effect was studied by considering a combined convective and rotating flow in a cylinder with a rotating lid and a parabolic temperature profile at the sidewall. Next, explanations of the destabilization effect for rotating-magnetic-field-driven flow and melt flow in a Czochralski crystal growth model were derived.

JFM classification

Convection: Buoyancy-driven instability Instability: Parametric instability Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 377 - 412
Copyright
Copyright © Cambridge University Press 2011

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Gelfgat supplementary movie

Movie 1. An example of cold thermals instability observed in experiments of Teitel et al. (2008) (for Fig. 5).

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Video 8.1 MB

Gelfgat supplementary movie

Movie 1. An example of cold thermals instability observed in experiments of Teitel et al. (2008) (for Fig. 5).

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Video 9.5 MB

Gelfgat supplementary movie

Movie 2. Cold thermals instability by superposition of base flow and perturbation (for Fig. 5).

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Video 6.9 MB

Gelfgat supplementary movie

Movie 2. Cold thermals instability by superposition of base flow and perturbation (for Fig. 5).

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Video 8.2 MB

Gelfgat supplementary movie

Movie 3. Cold thermals instability by solution of full non-linear problem (for Fig. 5).

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Video 7.8 MB

Gelfgat supplementary movie

Movie 3. Cold thermals instability by solution of full non-linear problem (for Fig. 5).

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Video 14.8 MB

Gelfgat supplementary movie

Movie 4. An example of the rotating (oscillatory) jet instability (for Fig. 12).

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Video 1.3 MB

Gelfgat supplementary movie

Movie 4. An example of the rotating (oscillatory) jet instability (for Fig. 12).

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Video 2 MB

Gelfgat supplementary movie

Movie 5. Isotherm oscillations for the cold thermals instability (for Fig. 13).

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Video 1.8 MB

Gelfgat supplementary movie

Movie 5. Isotherm oscillations for the cold thermals instability (for Fig. 13).

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Video 4.7 MB

Gelfgat supplementary movie

Movie 6. Isotherm oscillations for the cold thermals instability in Czochralski model flow without crystal rotation (for Fig. 17).

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Video 4.8 MB

Gelfgat supplementary movie

Movie 6. Isotherm oscillations for the cold thermals instability in Czochralski model flow without crystal rotation (for Fig. 17).

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Video 6.5 MB

Gelfgat supplementary movie

Movie 7. Isotherm oscillations for the cold thermals instability in Czochralski model flow with crystal rotation (for Fig. 18).

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Video 4.5 MB

Gelfgat supplementary movie

Movie 7. Isotherm oscillations for the cold thermals instability in Czochralski model flow with crystal rotation (for Fig. 18).

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Video 8 MB