April 3, 2009:  Shane Keating, CIMS

Diascalar diffusion: mixing and transport in a tracer-based coordinate system
  

  It is a curious fact that the scalar advection-diffusion equation exactly reduces to a simple 1D diffusion equation when written in a quasi-Lagrangian 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 Prandtl-Batchelor theorem, along with its extension to (potential) vorticity homogenization in geophysical and astrophysical flows.