April 3, 2009: Shane Keating, CIMS
Diascalar diffusion: mixing and transport in a
tracerbased coordinate system
It is a curious fact that the scalar advectiondiffusion equation exactly reduces to
a simple 1D diffusion equation when written in a quasiLagrangian coordinate system
aligned with the level set of the tracer field. In this informal talk, I plan to
review some recent results stemming from this observation. In particular, the
"diascalar diffusivity"  the diffusion coefficient appearing in the reduced
diffusion equation  offers a number of insights into the role of mixing barriers
and irreversible transport in atmospheric and oceanic turbulence. Finally, time and
patience permitting, I will discuss the connection between diascalar diffusivity and
the PrandtlBatchelor theorem, along with its extension to (potential) vorticity
homogenization in geophysical and astrophysical flows.
