Turbulent Boundary Layer Features via Lagrangian Coherent Structures, Proper Orthogonal Decomposition and Dynamic Mode Decomposition

TL;DR

This study combines Lagrangian coherent structures, Proper Orthogonal Decomposition, and Dynamic Mode Decomposition to analyze turbulent boundary layer features, revealing how flow structures relate to energy and frequency content.

Contribution

It introduces an integrated approach using LCS, POD, and DMD to visualize and understand turbulent boundary layer structures based on high-speed PIV data.

Findings

Longer LCS trajectories are linked to higher energy, lower frequency modes.

LCS trajectories highlight low momentum regions through multiple intersections.

Flow structures vary with advection time and mode characteristics.

Abstract

High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Re$_{\theta}$ 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.