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<p>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.</p>

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Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月6日

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  • Michele Coti Zelati,
  • Víctor Navarro-Fernández

摘要

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.