Eulerian and Lagrangian analysis of coherent structures in separated shear flow by time-resolved particle image velocimetry

Abstract

We investigate the turbulent shear flow that separates from a two-dimensional backward-facing step. We aim to analyze the unsteady separated and reattaching shear flow in both the Eulerian and Lagrangian frameworks in order to provide complementary insight into the self-sustaining coherent structures and Lagrangian transport of the entrainment process. The Reynolds number is Reh = 1.0 × 103, based on the incoming free-stream velocity and step height. The separated and reattaching shear flow as well as the recirculation region beneath is measured by time-resolved planar particle image velocimetry. As a result, time sequences of velocity vector fields in a horizontal–vertical plane in the center of the step model are obtained. In the Eulerian approach, a set of temporally orthogonal dynamic modes are extracted, and each one represents a single-frequency vortex pattern that neutrally evolves in time. The self-sustaining coherent structures are represented by reduced-order reconstruction of the identified high-amplitude dynamic modes, showing the basic unsteady flapping motion of the shear layer and the vortex rolling-up, pairing, and shedding processes superimposed on it. On the other hand, trajectories of passive fluid tracers depict the Lagrangian fluid transport by the entrainment process in the separated shear flow and identify the time-dependent vortex rolling-up process as well as complex vortex interactions. The contours of the finite-time Lyapunov exponent reveal the unsteady Lagrangian coherent structures that significantly shape the vortex patterns and contribute substantial parts to the fluid entrainment in the shear flow.