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- Resumen es exacto "Nonstationary wakes formed by the separation of the boundary layer of a bluff body are of interest in fluid dynamics, both from an academic viewpoint as well as from the point of view of applications. In these flows, in contrast to what happens in stationary cases, the analysis from the two perspectives that are relevant to describe the dynamics of a fluid –the Eulerian and the Lagrangian frames– produce non comparable predictions. Streaklines are associated to the Lagrangian formulation, and are defined as the set of particles passing through a fixed point in the past. They can be materialized in the laboratory through the injection of a passive tracer from a determined injection or seeding point, but they can also be identified outside the laboratory in some spill processes. In stationary fluids, streaklines coincide with streamlines, which are intrinsically linked to the Eulerian formulation. In such cases, two miscible blobs separated by a streamline will tend to mix through a process called diffusion. The mixing process, however, can be accelerated incorporating a nonstationary perturbation of the velocity, to impart an advective transport through the interface. The possibility of understanding this process, and of quantifying mixing, ranges from geophysical fluids to microfluidics, for example in assessing how a pollutant mixes with the surrounding fluid, or how a sample and a reagent can be mixed together effectively in reactor. This thesis introduces the use of topological time-series analysis through homologies as a diagnostic for Lagrangian dynamical diversity in fluid flows. This technique, developed in the framework provided by topology of chaos, is shown to constitute a powerful tool to understand transport phenomena. Branched Manifold analysis through Homologies (BraMAH) from time series enables computing the topology associated to a dynamical reconstruction. The analyzed time series correspond to the evolution of a scalar variable associated to an individual particle trajectory, as is the case of a coordinate position. The approach unravels the topological structure underlying the behavior of a fluid particle according to the dynamics that deploys within a finite time window. The effectiveness of the strategy is demonstrated with canonical case studies of kinematic flows that present transport barriers, as well as with the near wake of a cylinder that performs a rotary oscillation leading to non mixing islands that are unraveled for the first time in this thesis. The particules that are trapped into a non mixing island, are found to share the same homological description. The connection between the results of the topological analysis and the transport properties of the fluid is evidenced using streaklines."
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