DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Rich McLaughlin, University of North Carolina

**Title: ***
Passive scalar advection in parallel shear flows: WKBJ mode sorting
on intermediate times and the evolution of skewness
*

**Abstract:**
The evolution of a passive scalar diffusing in simple
parallel shear flows is a problem with a long history.
In 1953, GI Taylor showed theoretically and experimentally
that on long times, the passive scalar experiences an enhanced
diffusion in the longitudinal direction. On shorter times the
scalar evolution is anomalous, characterized by second moments
growing faster than linear in time as we show by analysis
of the stochastic differential equations underlying the passive
scalar equation. The spatial structures associated with this
intermediate time evolution are predicted using WKBJ analysis of
an associated non-self adjoint eigenvalue problem. This analysis
predicts a sorting of wall modes and interior modes with specific
predictions of the decay and propagation rates as a function of
the Peclet number. Monte-Carlo simulations and moment calculations
demonstrate non-trivial skewness evolution. Time permitting, new
behavior distinguishing channel from pipe flow will be presented
along with comparisons between some of these predictions and
experiments in the pipe geometry.
This work is joint with: Roberto Camassa, Zhi Lin, Keith Mertens,
Nick Moore, and Claudio Viotti

**Time:** Friday, Nov. 12, 2010, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491