Ghosh, S and Leonard, A. and Wiggins, S. (1998) Diffusion of a passive scalar from a no-slip boundary into a two-dimensional chaotic advection field. Journal of Fluid Mechanics, 372 . pp. 119-163. ISSN 0022-1120 http://resolver.caltech.edu/CaltechAUTHORS:GHOjfm98
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Using a time-periodic perturbation of a two-dimensional steady separation bubble on a plane no-slip boundary to generate chaotic particle trajectories in a localized region of an unbounded boundary layer flow, we study the impact of various geometrical structures that arise naturally in chaotic advection fields on the transport of a passive scalar from a local 'hot spot' on the no-slip boundary. We consider here the full advection-diffusion problem, though attention is restricted to the case of small scalar diffusion, or large Peclet number. In this regime, a certain one-dimensional unstable manifold is shown to be the dominant organizing structure in the distribution of the passive scalar. In general, it is found that the chaotic structures in the flow strongly influence the scalar distribution while, in contrast, the flux of passive scalar from the localized active no-slip surface is, to dominant order, independent of the overlying chaotic advection. Increasing the intensity of the chaotic advection by perturbing the velocity held further away from integrability results in more non-uniform scalar distributions, unlike the case in bounded flows where the chaotic advection leads to rapid homogenization of diffusive tracer. In the region of chaotic particle motion the scalar distribution attains an asymptotic state which is time-periodic, with the period the same as that of the time-dependent advection field. Some of these results are understood by using the shadowing property from dynamical systems theory. The shadowing property allows us to relate the advection-diffusion solution at large Peclet numbers to a fictitious zero-diffusivity or frozen-field solution, corresponding to infinitely large Peclet number. The zero-diffusivity solution is an unphysical quantity, but is found to be a powerful heuristic tool in understanding the role of small scalar diffusion. A novel feature in this problem is that the chaotic advection field is adjacent to a no-slip boundary. The interaction between the necessarily non-hyperbolic particle dynamics in a thin near-wall region and the strongly hyperbolic dynamics in the overlying chaotic advection field is found to have important consequences on the scalar distribution; that this is indeed the case is shown using shadowing. Comparisons are made throughout with the flux and the distributions of the passive scalar for the advection-diffusion problem corresponding to the steady, unperturbed, integrable advection field.
|Additional Information:||© 1998 Cambridge University Press. Received 10 June 1994 and in revised form 12 May 1998. We would like to acknowledge the parallel computing facilities made generously available by the Center for Advanced Computing Research at Caltech. This research was supported by a grant from the Air Force Office of Scientific Research, Grant No. AFOSR-91-0241 and by a grant from the Office of Naval Research, Grant No. N00014-97-1-0071.|
|Subject Keywords:||noise-reduction; enhancement; transport; flows|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||07 Jul 2009 22:20|
|Last Modified:||26 Dec 2012 10:53|
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