3D exponential mixing and fast dynamo effect with random ABC flows

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Víctor Navarro Fernández (Imperial College London)

Abstract: In this work we consider a time-periodic and random version of the Arnold-Beltrami-Childress (ABC) flow. We are concerned with two main subjects. On the one hand, we study the mixing problem of a passive tracer in the three dimensional torus by the action of the ABC vector field. On the other hand, we examine the effect of the ABC flows on the growth of a magnetic field described by the kinematic dynamo equations. To investigate these questions, we analyse the ABC flow as a random dynamical system and examine the ergodic properties of some associated Markov chains. This work settles that the random ABC vector field is an example of a space-time smooth universal exponential mixer in the three dimensional torus, and moreover, that it is an example of a nondissipative kinematic fast dynamo. This is a joint work with M. Coti Zelati (Imperial College London).