Reprint 901 Lagrangian Coherent Structures in Finite Domains

We develop a finite-domain finite-time Lyapunov exponent (FDFTLE) method to allow Lagrangian Coherent Structure (LCS) extraction from velocity data within limited domains. This removes spurious ridges as seen when trajectories are stopped at the domain boundaries. We find this extension useful in practical applications when LCS are extracted from LIDAR measurements at Hong Kong International Airport and used to determine airflow patterns around the airport. In addition to the FDFTLE method, we have developed a suite of mathematical tools to quantify different types of air motion near the LCS. This allows us to objectively describe the relative motion near LCS. INTRODUCTION The use of Lagrangian Coherent Structures (LCS) in the objective, frame-independent identification of transport and mixing structures in nonlinear fluid flows has been a popular trend in recent years [2, 4, 5, 7]. In the computation of the mathematical criteria that signifies LCS, initial conditions are integrated over time using a given velocity field to obtain the Lagrangian trajectory. Certain dynamical properties are evaluated along the trajectories to reveal Lagrangian coherence. For example, the finite-time Lyapunov exponent indicates the amount of stretching of nearby trajectories over a finite time considered [3]. In real applications, as a rule rather than exception, velocity fields are specified on open domains. This poses significant challenge in the computation of LCS when fluid trajectories meet the boundaries and leave the domain, since stopping the trajectories will artificially make the boundaries attractors and repellers, a false structure that is undesired. One way to mitigate the problem is artificially extending the data to a linear external velocity field. The external velocity is obtained by least square approximation of the given data in L2 norm while maintaining incompressibility. Velocity data and extrapolation are then connected by a filter function that smoothly FIGURE 1. Application of the FDFTLE method for an idealized flow