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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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.