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Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received January 29, 2006
Accepted July 12, 2006

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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The onset of Taylor-Gortler vortices in the time-dependent Couette flow induced by an impulsively imposed shear stress

Min Chan Kim^† Chang Kyun Choi¹

Department of Chemical Engineering, Cheju National University, Cheju 690-756, Korea ¹School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea

mckim@cheju.ac.kr

Korean Journal of Chemical Engineering, November 2006, 23(6), 874-880(7), 10.1007/s11814-006-0002-6

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Abstract

The onset of Taylor-Gortler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τc to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as Vi∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (Vi=constant). Based on the present τc and the Foster’s [1969] comment, the manifest stability guideline is suggested.

Keywords

Taylor-Gortler Vortex Time-Dependent Couette Flow Constant Shear Propagation Theory

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