Diagnosing transport and mixing using a tracer-based coordinate system

The advection-diffusion equation for the concentration of a tracer may be transformed into a pure diffusion equation by using the area inside concentration contours as a coordinate. The corresponding effective diffusivity depends on the geometry of the tracer field, which is determined by the underlying flow. Recent studies have used effective diffusivity, calculated from a suitable tracer, as a qualitative indicator of the transport and mixing properties of a given flow. Here we show that the effective diffusivity may further be used as a quantitative diagnostic of transport and mixing. We use a family of incompressible two-dimensional time-periodic flows as a test-bench and compare the calculated effective diffusivity with other diagnostics. The results demonstrate how the effective diffusivity accurately captures the location and character of barrier and mixing regions. We also show that the effective diffusivity parameterizes the transport of particles relative to the tracer-based coordinates. These results support the use of effective diffusivity as a quantifier of transport and mixing, and thereby strengthen the conclusions of previous qualitative studies. © 2003 American Institute of Physics. @DOI: 10.1063/1.1610471#