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.