Ghosh, S and Leonard, A. and Wiggins, S. (1998) Diffusion of a passive scalar from a noslip boundary into a twodimensional chaotic advection field. Journal of Fluid Mechanics, 372 . pp. 119163. ISSN 00221120. http://resolver.caltech.edu/CaltechAUTHORS:GHOjfm98

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Abstract
Using a timeperiodic perturbation of a twodimensional steady separation bubble on a plane noslip 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 noslip boundary. We consider here the full advectiondiffusion problem, though attention is restricted to the case of small scalar diffusion, or large Peclet number. In this regime, a certain onedimensional 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 noslip 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 nonuniform 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 timeperiodic, with the period the same as that of the timedependent 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 advectiondiffusion solution at large Peclet numbers to a fictitious zerodiffusivity or frozenfield solution, corresponding to infinitely large Peclet number. The zerodiffusivity 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 noslip boundary. The interaction between the necessarily nonhyperbolic particle dynamics in a thin nearwall 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 advectiondiffusion problem corresponding to the steady, unperturbed, integrable advection field.
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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. AFOSR910241 and by a grant from the Office of Naval Research, Grant No. N000149710071.  
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Subject Keywords:  noisereduction; enhancement; transport; flows  
Record Number:  CaltechAUTHORS:GHOjfm98  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:GHOjfm98  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  13683  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  07 Jul 2009 22:20  
Last Modified:  26 Dec 2012 10:53 
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