Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows
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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Fluid Dynamics and Turbulent Flows
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Journal of Dynamics and Differential Equations
- Volume
- 38
- Issue
- S1
- Pages
- 169–199
- Publication date
- 6 February 2026
- Language
- EN