This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.
We acknowledge funding from Netherlands (STW 11054; STW 10458; FOM 05PR2474) and Spain (FIS2013-48444-C2-1-P; FIS2013-48444-C2-2-P; FIS2016-77692-C2-1-P; FIS2016-77692-C2-2-P). This paper has grown out of the workshop “Physics of Mixing” organized by Cartwright, Clercx, van Heijst, and Speetjens, attended by those at the Lorentz Center, Leiden from 24 to 28 January 2011. We thank the Lorentz Center for its financial support and the Lorentz Center staff for making the workshop a great success. We acknowledge the three who are no longer with us, Hassan Aref, John Blake, and Slava (Viatcheslav) Meleshko, with whom we planned and worked on the paper.