Abstract
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph colouring and spectral graph drawing algorithms, examines a measure of the kinematic dissimilarity of all pairs of fluid trajectories, measured either experimentally, e.g. using particle tracking velocimetry, or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinematics remain similar throughout the time interval for which trajectory data are available, regardless of their physical proximity to one another. Through the use of several analytical and experimental validation cases, this algorithm is shown to robustly detect coherent structures using significantly less flow data than are required by existing spectral graph theory methods.
Highlights
The concept of coherence in fluid flows has historically been used to delineate packets of fluid elements that persist while the flow evolves without significant mixing with the surrounding fluid regions
We apply the coherent structure colouring (CSC) method to sparse trajectories derived from a particle image velocimetry (PIV) dataset of a long-strokeratio vortex ring, where secondary and tertiary rings in addition to a trailing jet form behind the primary vortex ring
This paper presents an algorithm for detecting coherence in flows where only sparse velocity data are available, as is often the case in particle tracking velocimetry, or oceanographic tracking of surface floats
Summary
The concept of coherence in fluid flows has historically been used to delineate packets of fluid elements that persist while the flow evolves without significant mixing with the surrounding fluid regions. Coherence can frequently be visualized qualitatively by observing the evolution of passive tracers in a flow (e.g. Huhn et al 2012; Haller 2015). Eulerian techniques for coherent structure identification include the q-criterion (Hunt, Wray & Moin 1988), λ2-criterion (Jeong & Hussain 1995) and the Okubo–Weiss parameter (Okubo 1970; Weiss 1991). All of these methods are frame-dependent, . Frame invariance is an important characteristic of a method for determining coherent structures. If a method identifies a structure boundary in one frame of reference, but not in another (for example, in a rotating reference frame), Coherent structure colouring the method may not be self-consistent in its characterization of fluid coherence (Haller 2005)
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