Lagrangian transport and chaotic advection in three-dimensional laminar flows

Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. While the more familiar turbulent flows promote efficient transport and mixing by their inherent spatio-temporal disorder, laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems, and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion ("advection") and the geometry, topology, and coherence of fluid trajectories. Efficient laminar transport being equivalent to "chaotic advection" is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows, yet the real world is three-dimensional (3D). Second, Lagrangian transport is typically investigated for idealized flows, yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilization of know-how on 3D Lagrangian transport and its dissemination to practice. To this end, 3D practical flows are categorized into canonical problems. First, to expose the diversity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the "Lagrangian mindset" into the analysis and design of 3D practical flows.