Geometric Skewness in the Passive Tracer Problem

The classic work by G.I. Taylor describes the enhanced longitudinal diffusivity of a passive tracer in laminar pipe flow. Much work since then has gone into extending this result particularly in calculating the evolution of the scalar variance. However, less work has been done to describe the asymmetry of the distribution. We present the results from a modeling effort for the general picture of how the higher moments of the tracer distribution depend on geometry. We do this via analysis of ``channel-limiting" geometries (rectangular ducts and elliptical pipes parameterized by their aspect ratio), using both new analytical tools and Monte-Carlo simulation, which have revealed a wealth of nontrivial behavior of the distributions at short and intermediate time.