A Topology-Based Method for Inferring Turbulence in Unsteady Flows

Abstract: Understanding the rise and evolution of turbulence is an important component of designing vehicles and turbomachinery that both have long life and are efficient. To this end, researchers study the complex phenomenon of turbulence. Free-stream turbulence against a flat plate is a common research area in fluid dynamics where one goal is to understand the transition from laminar to turbulent flow when colliding with a physical plate. There are several methods that have been tested, each based on a physical property of the flow, and each with respective advantages and disadvantages. One such issue is that of thresholding, which leads to flickering in animations. In this thesis, attempts to identify the turbulence is done by extracting the extrema of the flow data, followed by applying a Gaussian smoothing using Kernel Density Estimation to create a "density" field based on the spatial positions of the identified extrema. The method in this thesis is applied both in 2D and 3D, where the 3D results are visualized in both 2D and 3D perspectives. The results are then analyzed from the perspective of the smoothing method and compared against both earlier results from previous methods and the original data. Results of the method show that the extrema indeed can be be used to identify turbulent regions of the flow data. However, there were small turbulent regions visible in the original data that did not appear in the results of this thesis. When applying the kernel smoothing, a bandwidth (smoothing parameter) of 4:5 X 10-3 was used for the entire data set. Binary results from this choice of bandwidth were possible through thresholding, however, slight flickering is still observable. It is suggested that a larger bandwidth would give better results. The visual 3D results support the hypothesis that the extrema can be used to distinguish between laminar and turbulent regions of flow, and applying the smoothing method only on 2D slices gave better results when looking from a 2D perspective compared to the 3D method, which had some misleading results.