Finite-time scalar retention and slow mixing tails in uncertain passive-scalar transport
Citation Link: https://doi.org/10.15480/882.18911
Publikationstyp
Journal Article
Date Issued
2026-10-06
Sprache
English
TORE-DOI
Journal
Volume
38
Issue
10
Article Number
103606
Citation
Physics of Fluids 38 (10): 103606 (2026)
Publisher DOI
Scopus ID
Publisher
American Institute of Physics (AIP)
Peer Reviewed
true
Mixing of a passive scalar in a time-dependent flow is usually judged from the variance decay of a nominal flow. In many applications, though, stirring protocols and flow parameters are uncertain, and the more relevant question is whether the required level of homogenization is reached within a finite time. We study this reliability question for incompressible advection–diffusion with uncertain forcing parameters, using a time-periodic double-gyre flow as the main benchmark and a periodically stirred cavity as a secondary test. Direct numerical simulations show that delayed mixing is not a fluctuation around the mean variance decay curve. Instead, slow realizations retain coherent scalar remnants near weakly exchanging regions of the flow, which produces a persistent upper tail in the mixing time distribution. To identify these slow events without running a full simulation for every parameter sample, we build a parameter- and phase-dependent reduced transport operator by combining a proper orthogonal decomposition-based Koopman representation with a polynomial-chaos expansion in the uncertain parameters. From this operator, we compute a finite-time scalar-retention score based on the leading singular direction of the learned propagator in a scalar-energy metric. The diagnostic ranks parameter realizations by their tendency to retain scalar energy, identifies the realizations contributing to the upper tail of the mixing time distribution, and recovers the scalar structures responsible for delayed homogenization. Reliable mixing under uncertainty is therefore controlled not only by the mean variance decay, but also by the least-damped scalar directions of the uncertain transport operator, which suggests that designs targeting reliable mixing should act on these directions directly.
DDC Class
530.42: Fluid Physics
519: Applied Mathematics, Probabilities
Publication version
publishedVersion