Flow Topology and Tomography for Vortex Identification in Unsteady and in Three-Dimensional Flows

The characterization of organized structures is discussed with emphasis on changes of the flows topologies. The changes may be monitored in physical space. However, structural changes also appear in the space of invariants of various vector-gradient tensor. Vortices are only one part of a flow structure to be identified herewith. Jacobian invariants of vector-field mappings onto physical space provide a topological characterization of flow structures and their changes in physical and in the vector-field spaces. Several problems of structure identification are high-lighted with respect to instantaneous flow fields and within cross-sectional flow patterns of iso-surfaces of any scalars or components of vectors. On the other hand, the topological structures of flows (defined by any physical vector quantity of interest) are well-defined by singular flow surfaces in physical space. However, their geometric complexity in three-dimensional and/or unsteady flows suggests to monitor especially their local genesis occuring at higher-order degeneracies in physical space and/or singularities in spaces of components and/or invariants of vector-fields. Flow tomography is suggested to provide a means for flow analyses in physical spac