Lagrangian description and quantification of scalar mixing in fluid flows from particle tracks

Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures that determine material transport, including recent data-based methods that aim to identify such coherent objects directly from tracer trajectories. These methods have helped to gain a better understanding of the underlying dynamics. However, the quantification of scalar mixing has not been the focus. Here, we develop a data-driven description and quantification of transport and mixing of scalar quantities by combining a diffusion map approach for the extraction of coherent flow structures with aspects of deterministic particle methods.