Understanding wake structure and vortex formation is important to improve the flight performance of the bio-inspired micro-air vehicles (MAVs). The traditional method to detect vortex structure and boundaries is using vorticity, which subject to arbitrary chosen of a criterion value. A more objective criterion of identifying vortex boundaries is Lagrangian coherent structure (LCS) based on the local maxima (ridges) of finite-time Lyapunov exponent (FTLE) field. The FTLE measures the maximum growth rate of the perturbation distance x between adjacent fluid particles over the time interval T. It characterizes the amount of stretching or separation during a specified time interval (t, t+T). Attracting LCS is indicated by the ridges (high values) of backward-time FTLE, which is computed by integrating the flow field in reverse time. The fluid particles tend to align with the attracting LCS over time. LCS is used to identify the vortex structure and understand vortex formation in the wake generated by flapping wings. With the help of tracer particles, the process of vortex formation can also be explored.

Vorticity of 2D hovering plate

LCS of 2D hovering plate