2018/08/14 by George Haller, Daniel Karrasch, Florian Kogelbauer
Engineering · Mathematics · Physics and Astronomy · #Advection #Classical mechanics #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Mathematics #Mechanics #Observable #Physics #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #Statistical physics #Tensor (intrinsic definition) #Thermal diffusivity #Thermodynamics #math.DS #nlin.CD #physics.ao-ph #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.1073/pnas.1720177115
published as PNAS September 11, 2018 115 (37) 9074-9079 · Accepted, non-copyedited version (Proceedings of the National Academy of Sciences)
arxiv created 2018/08/14 · openalex publication_date 2018/08/27 · arxiv updated 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.