Classification of Langrangian tracer trajectories in 3D fluid turbulence
In fluid dynamics, computer simulations have become an invaluable tool to study the effects of turbulence in fluid motion. Especially direct numerical simulations provide the means to observe turbulence in great detail. However, the vast amounts of data produced make statistical analysis difficult, if time and manpower are scarce. To gather relevant information, automatic feature extraction becomes a necessity.
This thesis presents an approach for automatic classification of Lagrangian tracer trajectories in 3D fluid turbulence using discrete wavelet transform as a basis for feature extraction. A typical phenomenon of turbulent fluid motion is the vortex, describing a swirling motion around a common axis of rotation. Its oscillating movements become visible in the lateral accelerationn of a particle tracer, conceptually causing regions of increased energy in the coefficients of a discrete wavelet transform, which in conjunction with statistical considerations build the basis for an automatic vortex detection.
Subsequently, an unsupervised cluster analysis built on different measures of similarity is performed, trying to uncover significant structure and generative processes within the data.