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Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows
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In this work we consider the Lagrangian properties of a random version of the Arnold-Beltrami-Childress (ABC) 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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Cited by 1 Pith paper
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Exponentially mixing flows with slow enhanced dissipation
Random alternating shear flows on the torus mix exponentially with diffusivity-independent rates yet have dissipation time of order 1/κ, showing enhanced dissipation is not implied by exponential mixing for merely C0 flows.
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