Vortex-induced chaotic mixing in wavy channels
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Published Version
Date
2010-07-10
Authors
Lee, Wei-Koon
Taylor, P. H.
Borthwick, Alistair G. L.
Chuenkum, S.
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
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Abstract
Mixing is studied in open-flow channels with conformally mapped wavy-wall profiles,
using a point-vortex model in two-dimensional irrotational, incompressible mean flow.
Unsteady dynamics of the separation bubble induced by oscillatory motion of point
vortices located in the trough region produces chaotic mixing in the Lagrangian
sense. Significant mass exchange between passive tracer particles inside and outside
of the separation bubble forms an efficient mixing region which evolves in size as
the vortex moves in the unsteady potential flow. The dynamics closely resembles that
obtained by previous authors from numerical solutions of the unsteady Navier–Stokes
equations for oscillatory unidirectional flow in a wavy channel. Of the wavy channels
considered, the skew-symmetric form is most efficient at promoting passive mixing.
Diffusion via gridless random walks increases lateral particle dispersion significantly
at the expense of longitudinal particle dispersion due to the opposing effect of mass
exchange at the front and rear of the particle ensemble. Active mixing in the wavy
channel reveals that the fractal nature of the unstable manifold plays a crucial role
in singular enhancement of productivity. Hyperbolic dynamics dominate over nonhyperbolicity
which is restricted to the vortex core region. The model is simple yet
qualitatively accurate, making it a potential candidate for the study of a wide range
of vortex-induced transport and mixing problems.
Description
Keywords
Wavy channel , Separation bubble , Wavy-wall , Flow
Citation
WEI-KOON LEE, P. H. TAYLOR, A. G. L. BORTHWICK and S. CHUENKHUM (2010). Vortex-induced chaotic mixing in wavy channels. Journal of Fluid Mechanics, 654 , pp 501-538 doi:10.1017/S0022112010000674
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© Cambridge University Press 2010