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math.AP2026
Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives
Kyle L. Liss, Kunhui Luan
We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with fin…
math.AP2026
The Batchelor spectrum for a deterministically driven passive scalar
Kyle L. Liss, Jonathan C. Mattingly
We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and t…
math.AP2024
A pathwise approach to the enhanced dissipation of passive scalars advected by shear flows
Victor Gardner, Kyle L. Liss, Jonathan C. Mattingly
We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential…