Numerical Evidence of Exponential Mixing by Alternating Shear Flows

2021/10/29 by Li‐Tien Cheng, Frederick Rajasekaran, Cheng, Li-Tien +5 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2111.00093

openalex publication_date 2021/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We performed a numerical study of the efficiency of mixing by alternating horizontal and vertical shear ``wedge'' flows on the two-dimensional torus. Our results suggest that except in cases where each individual flow is applied for only a short time, these flows produce exponentially fast mixing. The observed mixing rates are higher when the individual flow times are shorter (but not too short), and randomizing either the flow times or phase shifts of the flows does not appear to enhance mixing (again when the flow times are not too short). In fact, the latter surprisingly seems to inhibit it slightly.

Citations

• A Lemma and a Conjecture on the Cost of Rearrangements

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