Junior Analysis Seminar – Augusto Del Zotto (Zurich)

We exhibit an incompressible velocity field on the two-dimensional unit sphere such that the time evolution of any mean-free initial data passively advected by the velocity field is mixed exponentially fast. In the presence of molecular diffusivity, we show that the solution to the associated advection-diffusion equation experiences enhanced dissipation with optimal decay rates. The mixing velocity field is an alternating combination of two Rossby-Haurwitz flows with random amplitudes and constitutes a spherical analogue to the sine shear-alternating example of Pierrehumbert.
This is a joint work with Marc Nualart (ICMAT).