DIFFUSION OF A PASSIVE SCALAR FROM A NO-SLIP BOUNDARY INTO A 2-DIMENSIONAL CHAOTIC ADVECTION FIELD

Citation
S. Ghosh et al., DIFFUSION OF A PASSIVE SCALAR FROM A NO-SLIP BOUNDARY INTO A 2-DIMENSIONAL CHAOTIC ADVECTION FIELD, Journal of Fluid Mechanics, 372, 1998, pp. 119-163
Citations number
43
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanics,"Phsycs, Fluid & Plasmas
Journal title
ISSN journal
0022-1120
Volume
372
Year of publication
1998
Pages
119 - 163
Database
ISI
SICI code
0022-1120(1998)372:<119:DOAPSF>2.0.ZU;2-2
Abstract
Using a time-periodic perturbation of a two-dimensional steady separat ion bubble on a plane no-slip boundary to generate chaotic particle tr ajectories in a localized region of an unbounded boundary layer flow, we study the impact of various geometrical structures that arise natur ally 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 th e case of small scalar diffusion, or large Peclet number. In this regi me, a certain one-dimensional unstable manifold is shown to be the dom inant organizing structure in the distribution of the passive scalar. In general, it is found that the chaotic structures in the flow strong ly influence the scalar distribution while, in contrast, the flux of p assive scalar from the localized active no-slip surface is, to dominan t order, independent of the overlying chaotic advection. Increasing th e intensity of the chaotic advection by perturbing the velocity held f urther away from integrability results in more non-uniform scalar dist ributions, unlike the case in bounded flows where the chaotic advectio n 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 b y using the shadowing property from dynamical systems theory. The shad owing 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-d iffusivity solution is an unphysical quantity, but is found to be a po werful heuristic tool in understanding the role of small scalar diffus ion. A novel feature in this problem is that the chaotic advection fie ld is adjacent to a no-slip boundary. The interaction between the nece ssarily non-hyperbolic particle dynamics in a thin near-wall region an d the strongly hyperbolic dynamics in the overlying chaotic advection field is found to have important consequences on the scalar distributi on; that this is indeed the case is shown using shadowing. Comparisons are made throughout with the flux and the distributions of the passiv e scalar for the advection-diffusion problem corresponding to the stea dy, unperturbed, integrable advection field.