Material barriers to diffusive and stochastic transport

Proceedings of the National Academy of Sciences of the United States of America
George HallerFlorian Kogelbauer

Abstract

We seek transport barriers and transport enhancers as material surfaces across which the transport of diffusive tracers is minimal or maximal in a general, unsteady flow. We find that such surfaces are extremizers of a universal, nondimensional transport functional whose leading-order term in the diffusivity can be computed directly from the flow velocity. The most observable (uniform) transport extremizers are explicitly computable as null surfaces of an objective transport tensor. Even in the limit of vanishing diffusivity, these surfaces differ from all previously identified coherent structures for purely advective fluid transport. Our results extend directly to stochastic velocity fields and hence enable transport barrier and enhancer detection under uncertainties.

References

Apr 8, 2010·Chaos·Thomas Peacock, John Dabiri
Apr 29, 2011·Nature·Lisa M BealUNKNOWN SCOR/WCRP/IAPSO Working Group 136
Jun 3, 2016·Chaos·Mattia Serra, George Haller
Nov 3, 2016·Chaos·Alireza Hadjighasem, George Haller
Jun 4, 2017·Chaos·Alireza HadjighasemGeorge Haller

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Citations

Dec 25, 2019·Physical Review. E·Christiane SchneideJörg Schumacher
Jul 12, 2020·Proceedings of the National Academy of Sciences of the United States of America·Jacob O WenegratCraig M Lee

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