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Higher-order boundary-layer solution for unsteady motion of a circular cylinder

Published online by Cambridge University Press:  26 April 2006

Soonil Nam
Soonil Nam
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

The higher-order boundary-layer solution for an impulsively started circular cylinder with uniform velocity and for an exponentially accelerating cylinder in incompressible, relatively high-Reynolds-number flow of short duration are considered. A perturbation method is employed to linearize the two-dimensional vorticity transport equation by a double series expansion with respect to the Reynolds number and the time. A matched asymptotic expansion is carried out to define the proper boundary conditions between the viscous and inviscid layers for the linearized first-, second-, and third-order boundary-layer equations. Singularities appear in the higher-order approximate solutions to the viscous displacement velocities and skin frictions, which coincide with the singularity of the first-order approximate solution. These singularities have alternating signs and increasing magnitudes, thus attempting to remove the effects of the singularity of the lower-order solution. However, this futile attempt at removing a singularity by superposing even stronger singularities makes the solution worse around the singularity, which shows that the singularity is an artifact of the thin-boundary-layer approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 89 - 110
Copyright
© 1990 Cambridge University Press

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