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Updated: Oct 15, 2026

Quantifying Mixing using Magnetic Resonance Imaging
Published on: January 25, 2012
Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows
Michele Coti Zelati1, Víctor Navarro-Fernández1
1Department of Mathematics, Imperial College London, LONDON, SW7 2AZ UK.
Abstract:
In this work we consider the Lagrangian properties of a random version of the Arnold-Beltrami-Childress (ABC) flows in a three-dimensional periodic box. We prove that the associated flow map possesses a positive top Lyapunov exponent and its associated one-point, two-point and projective Markov chains are geometrically ergodic. For a passive scalar, it follows that such a velocity is a space-time smooth exponentially mixing field, uniformly in the diffusivity coefficient. For a passive vector, it provides an example of a universal ideal (i.e. non-diffusive) kinematic dynamo.
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