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The evolution of a localized vortex disturbance in external shear flows. Part 1. Theoretical considerations and preliminary experimental results

Published online by Cambridge University Press:  26 April 2006

Vladimir Levinski  and
Jacob Cohen
Vladimir Levinski
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Jacob Cohen
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
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Abstract

The evolution of a finite-amplitude three-dimensional localized disturbance embedded in external shear flows is addressed. Using the fluid impulse integral as a characteristic of such a disturbance, the Euler vorticity equation is integrated analytically, and a system of linear equations describing the temporal evolution of the three components of the fluid impulse is obtained. Analysis of this system of equations shows that inviscid plane parallel flows as well as high Reynolds number two-dimensional boundary layers are always unstable to small localized disturbances, a typical dimension of which is much smaller than a dimensional length scale corresponding to an O(1) change of the external velocity. Since the integral character of the fluid impulse is insensitive to the details of the flow, universal properties are obtained. The analysis predicts that the growing vortex disturbance will be inclined at 45° to the external flow direction, in a plane normal to the transverse axis. This prediction agrees with previous experimental observations concerning the growth of hairpin vortices in laminar and turbulent boundary layers. In order to demonstrate the potential of this approach, it is applied to Taylor-Couette flow, which has additional dynamical effects owing to rotation. Accordingly, a new instability criterion associated with three-dimensional localized disturbances is found. The validity of this criterion is supported by our experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 159 - 177
Copyright
© 1995 Cambridge University Press

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