We use direct Lyapunov exponents (DLE) to identify Lagrangian coherent structures in two different three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. We find that despite additional computational cost, the DLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. As a further advantage, the DLE method requires no velocity derivatives, which are often too noisy to be useful in the study of a turbulent flow. We study the evolution of a single hairpin vortex into a packet of similar structures, and show that the birth of a secondary vortex corresponds to a loss of hyperbolicity of the Lagrangian coherent structures.

Particle image velocimetry (PIV) is used to investigate the three-dimensional wakes of rigid pitching panels with a trapezoidal geometry, chosen to model idealized fish caudal fins. Experiments are performed for Strouhal numbers from 0.17 to 0.56 for two different trailing edge pitching amplitudes. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von Kármán vortex street pattern is observed along the mid-span of the near wake, but the vortices realign and exhibit strong interactions near the spanwise edges of the wake. At higher Strouhal numbers, the complexity of the wake increases downstream of the trailing edge as the spanwise vortices spread transversely and lose coherence as the wake splits. This wake transition is shown to correspond to a qualitative change in the LCS pattern surrounding each vortex core, and can be identified as a quantitative event that is not dependent on arbitrary threshold levels. The location of this transition is observed to depend on both the pitching amplitude and free stream velocity, but is not constant for a fixed Strouhal number. On the panel surface, the trapezoidal planform geometry is observed to create additional vortices along the swept edges that retain coherence for low Strouhal numbers or high sweep angles. These additional swept-edge structures are conjectured to add to the complex three-dimensional flow near the tips of the panel.

We use direct Lyapunov exponents to identify Lagrangian coherent structures (LCSs) in a bioinspired fluid flow: the wakes of rigid pitching panels with a trapezoidal planform geometry chosen to model idealized fish caudal fins. When compared with commonly used Eulerian criteria, the Lagrangian method has previously exhibited the ability to define structure boundaries without relying on a preselected threshold. In addition, qualitative changes in the LCS have previously been shown to correspond to physical changes in the vortex structure. For this paper, digital particle image velocimetry experiments were performed to obtain the time-resolved velocity fields for Strouhal numbers of 0.17 and 0.27. A classic reverse von Kármán vortex street pattern was observed along the midspan of the near wake at low Strouhal number, but at higher Strouhal number the complexity of the wake increased downstream of the trailing edge. The spanwise vortices spread transversely across the wake and lose coherence, and this event was shown to correspond to a qualitative change in the LCS at the same time and location.

To understand the fluid dynamics of a biologically inspired unsteady low-aspect-ratio propulsor, unsteady pressure distributions were measured and compared with time-averaged thrust performance and wake visualizations. The experiments were performed on rigid rectangular panels with different aspect ratios, pitching in a uniform flow. Panel aspect ratio and pitching amplitude were shown to affect the magnitude and time dependence of the pressure distribution on the panel surface, the vorticity generation on the panel, and thrust production. A new scaling is proposed that includes these parameters and collapses the oscillating pressure magnitude and the thrust coefficient.

The wake behind a circular cylinder is studied to investigate the complex vortex shedding physics in the near-wake region. Both the Q criterion and a Lagrangian coherent structure analysis are appl...