Lagrangian Dynamics in Two-Dimensional Flow
Nicholas T. Ouellette
Department of Mechanical Engineering, Yale University
Any continuum system can described in two complementary frameworks: the Eulerian approach, where we consider field variables, and the Lagrangian approach, where instead we consider the dynamics of particles that are passively advected by the continuum flow. True Lagrangian measurements have only recently become possible, and they have become a powerful tool for investigating complex fluid flow. I will illustrate these techniques with two examples, measured in a quasi-two-dimensional laboratory flow that exhibits spatiotemporal chaos. First, by measuring the curvature of fluid element trajectories, we have developed a robust way of studying the topology of the flow and have found an apparent connection between topology and the onset of spatiotemporal chaos. Second, we have extended our methods to study the dynamics of transported particles that do not follow the flow, as a function of both particle size and shape.