SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 1, Page 85-123, January 2020.
Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located directly from the deterministic component of the velocity field without diffusive or stochastic simulations. Here we extend these results to compressible flows and to diffusive concentration fields affected by sources or sinks, as well as by spontaneous decay. We construct diffusive transport extremizers with and without constraining them on a specific initial concentration distribution. For two-dimensional flows, we obtain explicit differential equations and a diagnostic scalar field that identify the most observable extremizers with pointwise uniform transport density. We illustrate our results by uncovering diffusion barriers and enhancers in analytic, numerical, and observational velocity fields.

中文翻译：

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可压缩流中扩散标量的传输障碍

SIAM应用动力系统杂志，第19卷，第1期，第85-123页，2020年1月。
我们最近的工作确定了不可压缩流中的物质表面，这些物质表面将相对于相邻表面的任意弱扩散标量场的传输极端化了。可以直接从速度场的确定性分量定位此类传输的障碍和增强器，而无需进行扩散或随机模拟。在这里，我们将这些结果扩展到可压缩流和受源或汇以及自发衰减影响的扩散浓度场。我们构造带有或不约束特定初始浓度分布的扩散运输极端子。对于二维流，我们获得了显式微分方程和诊断标量场，该标量场标识了具有逐点均匀传输密度的最可观察到的极端子。