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Streak evolution in viscoelastic Couette flow

Published online by Cambridge University Press:  21 February 2014

Jacob Page  and
Tamer A. Zaki
Jacob Page
Affiliation:
Department of Mechanical Engineering, Imperial College, London SW7 2AZ, UK
Tamer A. Zaki
Affiliation:
Department of Mechanical Engineering, Imperial College, London SW7 2AZ, UK
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Abstract

The combined effect of inertia and elasticity on streak amplification in planar Couette flow of an Oldroyd-B fluid is examined. The linear perturbation equations are solved in the form of a forced-response problem to obtain the wall-normal vorticity response to a decaying streamwise vortex. With significant disparity between the solvent diffusion and polymer relaxation time scales, two distinct responses are possible. The first is termed ‘quasi-Newtonian’ because the streak evolution collapses onto the Newtonian behaviour at the same total and solvent Reynolds numbers when relaxation is very fast or slow, respectively. The second response is labelled ‘elastic’: with a long relaxation time, the streaks can reach significant amplitudes even with very weak inertia. If the diffusion and relaxation time scales are commensurate, the streaks are able to re-energize in a periodic cycle within an envelope of overall decay. This behaviour is enhanced in the instantaneously elastic limit, where the governing equation reduces to a forced wave equation. The streak re-energization is demonstrated to be a superposition of trapped vorticity waves.

JFM classification

Instability: Transition to turbulence Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 520 - 551
Copyright
© 2014 Cambridge University Press 

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