Computer Science Senior Thesis

Two methods for the identification of coherent structures in fluid flows are studied for possible combination in a hybrid method providing deeper insight and greater efficiency. One method uses wavelet transforms to partition the field into coherent and incoherent portions using a thresholding of the wavelet coefficients. The other method is based on the stability analysis of trajectories through the fluid, defining two type of Lagrangian coherent structures based on the degree hyperbolicity or ellipticity of the flow. It is hoped that computational efficiency of the wavelet method can be combined with the level of detail of the stability analysis to give a fast and insightful method for analyzing and identify coherent structures in a flow. Two types of tests are done to determine the feasibility of combining the two methods. The first test is used to determine the degree to which the coherent partition from the wavelet method agrees with the Lagrangian coherent structures of the stability analysis method. The second test is used to determine how suitable the coherent partition of the wavelet coefficients is for guiding the efficient placement of the tracers used by the stability analysis method. The results from the first test do not indicate a connection between the coherent wavelet partition and Lagrangian coherent structures, and also indicate that the wavelet method is susceptible to regions of high shear. The results from the second test show that basic methods for placing tracers based on the coherent wavelet partition do not perform better than a uniform distribution of particles throughout the flow. Overall, the results do not indicate that a combinations of the two methods will be beneficial, but that there are a number of possible future directions that warrant further pursuit of the topic.