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

Thursday, April 15, 2010 - 3:00pm - 3:45pm
EE/CS 3-180
Richard McLaughlin (University of North Carolina, Chapel Hill)
Keywords: mixing, shear dispersion, Taylor dispersion

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 demonstrate non-trivial skewness evolution, and skewness is studied in the new WKBJ modes. 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 is joint work with Roberto Camassa, Zhi Lin, Keith Mertens, Nick Moore, and Claudio Viotti.
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