%0 Journal Article
%A Haller, George
%A Karrasch, Daniel
%A Kogelbauer, Florian
%T Material barriers to diffusive and stochastic transport
%D 2018
%R 10.1073/pnas.1720177115
%J Proceedings of the National Academy of Sciences
%P 9074-9079
%V 115
%N 37
%X Observations of tracer transport in fluids generally reveal highly complex patterns shaped by an intricate network of transport barriers and enhancers. The elements of this network appear to be universal for small diffusivities, independent of the tracer and its initial distribution. Here, we develop a mathematical theory for weakly diffusive tracers to predict transport barriers and enhancers solely from the flow velocity, without reliance on diffusive or stochastic simulations. Our results yield a simplified computational scheme for diffusive transport problems, such as the estimation of salinity redistribution for climate studies and the forecasting of oil spill spreads on the ocean surface.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.
%U https://www.pnas.org/content/pnas/115/37/9074.full.pdf