Using braids to quantify interface growth and coherence in a rotor-oscillator flow

Abstract

The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics, and can also be used to identify regions of coherence. Estimating such growth rates can be difficult, since they depend on detailed properties of the velocity field, such as its derivatives, that are hard to measure directly. When an experiment gives only sparse trajectory data, it is natural to encode planar trajectories as mathematical braids, which are topological objects that contain information on the mixing characteristics of the flow, in particular through their action on topological loops. We test such braid methods on an experimental system, the rotor-oscillator flow, which is well-described by a theoretical model. We conduct a series of laboratory experiments to collect particle tracking and particle image velocimetry data, and use the particle tracks to identify regions of coherence within the flow that match the results obtained from the model velocity field. We then use the data to estimate growth rates of material interface, using both the braid approach and numerical simulations. The interface growth rates follow similar qualitative trends in both the experiment and model, but have significant quantitative differences, suggesting that the two are not as similar as first seems. Our results shows that there are challenges in using the braid approach to analyze data, in particular the need for long trajectories, but that these are not insurmountable.

arXiv comment18 pages including Supplementary Material, 16 figures. RevTeX 4.1 document class

References in corpus (28)

• Frontiers of chaotic advection
• A Critical Comparison of Lagrangian Methods for Coherent Structure Detection
• A Spectral Clustering Approach to Lagrangian Vortex Detection
• Using multiscale norms to quantify mixing and transport
• Coherent sets for nonautonomous dynamical systems
• Thirty Years of Turnstiles and Transport
• Detecting coherent structures using braids
• Topological Mixing with Ghost Rods
• Braids of entangled particle trajectories
• Coherent structure coloring: identification of coherent structures from sparse data using graph theory
• Efficient algorithm for detecting unstable periodic orbits in chaotic systems
• Topology, Braids, and Mixing in Fluids
• Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
• Measuring Topological Chaos
• On the complexity of braids
• Finite-Time Braiding Exponents
• Stretching and Curvature of Material Lines in Chaotic Flows
• Topological optimisation of rod-stirring devices
• Geometrical Constraints on Finite-time Lyapunov Exponents in Two and Three Dimensions
• Topological Entropy of Braids on the Torus
• Topological Chaos in Spatially Periodic Mixers
• Topological chaos, braiding and bifurcation of almost-cyclic sets
• The mathematics of taffy pullers
• Ensemble-based Topological Entropy Calculation (E-tec)
• Quantifying the Tangling of Trajectories Using the Topological Entropy
• Shape Coherence and Finite-Time Curvature Evolution
• Variational assimilation of Lagrangian data in oceanography
• Mesochronic classification of trajectories in incompressible 3D vector fields over finite times