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Pietro Cassottana
The study of coherent motions emerging in the chaotic background of turbulent flows is an active branch of research, motivated primarily by the need of developing predictive models for the main statistics of turbulent flows and provide new tools of analysis to the control of turbulence. While the existence of such deterministic coherent structures has been known for a long time, their definition is still an open question as there is no universal agreement on what really is a coherent structure.In this work, a definition of Lagrangian coherent structures based on the computation of the finite-time Lyapunov exponent is considered. Such definition presents advantages with respect to those from which Eulerian criteria to vortex identification take inspiration. It represents a frame-independent definition, essential in the case of rotating flows and flows with interacting vortices. On the base of this definition, a numerical scheme for the detection and tracking of Lagrangian coherent structures is developed. The method identifies repelling and attracting material lines which determine the location of the boundaries of coherent structures objectively and without the need of fixing a threshold, partitioning the domain based on the value of some function. The Lagrangian method is tested on a three-dimensional, analytically defined flow with non-trivial streamline geometry for which similar analysis are reported in the literature.
Two physically relevant and widely studied test cases are also analyzed using the Lagrangian approach. Lagrangian coherent structures are detected in a fully turbulent channel flow, with special focus on the structures that populate the near-wall region. A comparison is carried out between the result for a time-varying flow and a frozen flow, described by the velocity field associated to a single time instant. The Lagrangian behaviour of the these structures is evidenced. For a turbulent flow in a channel that presents a bump on the lower wall, two widely used Eulerian criteria to vortex identification are compared with the Lagrangian definition. It is shown that the latter method is able to succeed where the former ones do not agree or fail completely in detecting vortex cores.