This work is funded by the National Science Foundation (NSF-CBET-1034581).
Turbulent boundary layer, Lagrangian functions, Flows (Differentiable dynamical systems), Orthogonal decompositions, Decomposition (Mathematics)
High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Reθ of 9800 in order to elucidate the coherent structures. Snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to visualize the flow structure depending on the turbulent kinetic energy and frequency content. The first six POD and DMD modes show the largest and the lowest amount of energy and frequency, respectively. Lagrangian coherent structure (LCS) based on the algorithm developed using the variational theory is also applied to track the flow via attracting and repelling trajectories. The shapes and the length of the trajectories show variation with increasing advection time. LCS trajectories are overlayed with the individual POD and DMD modes. Repelling and attracting lines cover the structure of these modes. Reconstructed flow fields from individual POD modes are also used to generate new LCS trajectories. The energy and frequency content have a direct impact on the length of the trajectories, where the longest reconstructed trajectories associate with the higher energy and lower frequency modes, and vise verse. The multiple intersection points between the repelling and attracting lines marked the low momentum regions.
Ali, N., Tutkun, M., & Cal, R. B. (2017). Turbulent Boundary Layer Features via Lagrangian Coherent Structures, Proper Orthogonal Decomposition and Dynamic Mode Decomposition. arXiv preprint arXiv:1704.04090.