a1 Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
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 non-hyperbolicity 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.
(Received May 14 2009)
(Revised January 11 2010)
(Accepted February 02 2010)
(Online publication May 11 2010)