Kinematics of vortices in turbulent flows

We analyze the currently popular vortex-identification criteria that are based on point-wise analysis of the velocity gradient tensor. We introduce a new measure of spiraling compactness of material orbits in vortices and use this measure to propose a new local vortex-identification criterion and requirements for a vortex core. Using both zero and non-zero thresholds for the identification parameter, we explore analytically the interrelationships between the different criteria. These interrelationships provide a new interpretation of the various criteria in terms of the local flow kinematics. We study three canonical turbulent flow examples and observe that all the criteria, given the proposed usage of threshold, result in remarkably similar-looking vortical structures. We offer a unified interpretation based on local flow kinematics for the conditions under which similarity or differences can be expected in the vortical structures educed using the different criteria.; The commonly used local vortex-identification criteria are formulated based on some characteristics of a vortex that is isolated from any effects of other vortical and strain fields. Nevertheless, these criteria have been frequently used for extracting vortical structures in complex flows in which the vortices are curved (self-interaction) and/or are in close proximity to each other (mutual-interaction). We study the effects of such interactions on the validity of the usage of local criteria for extracting the vortices. Our study is a posteriori in nature: we construct flow fields based on vortex interactions and then use vortex criteria to extract the constituent vortices. We find that self-interaction does not drastically affect vortex identification, whereas mutual interaction may significantly affect the extracted vortex structure. We propose a simple model that may be used to predict the effects of mutual interaction on the vortex structure extracted by the different vortex criteria.; The concept of a hierarchy of vortices in the physical space of turbulent flows is commonly extended to Fourier space. Through an analysis of Gaussian vortices, we explore the concept a vortex in Fourier space in terms of local flow kinematics. We find that interpreting a hierarchy of vortices in Fourier space may lead to incorrect results.