Analyse de champs de vitesse par FTLE à partir de la méthode des moments : validation théorique et expérimentale

Abstract : With the development of technology, instantaneous flow fields coming from experiments or numerical simulation are available now. It has been followed by a rise of interest for the Lagrangian analysis of such data. One central tool to analyze the flow fields is the Finite Time Lyapunov Exponent (FTLE). It allows to the identify of the Lagrangian Coherent Structures (LCS) which appear as ridges in the FTLE fields. The LCS are quasi transport bareers and separatte the fluid domain into regions which have different dynamic properties. However, the computation methodology currently used in order to obtain the FTLE requires numerical evalution of a large number of fluid particle trajectories on cartesian or adaptive meshes that are superimposed on the original data grid.In this thesis, we propose a new method for calculating the Finite Time Lyapunov Exponent FTLE fields. For this, we use the method of second-order moments which allows to evaluate over time the dispersion of particles uniformly distributed in a circular or elliptical domain. We call this new scalar field, the M-FTLE field. We validate this approach theoretically, at every point of the fluid domain by comparing FTLE and M-FTLE and also by the comparison of the classic examples (linear velocity field, circular and hyperbolic) and a numerical example (velocity field of double gyre). This method is then applied on experimental measurements of tidal bore velocity fields, obtained within the institute 'Pprime' by using a measurement technique called particle image velocimetry (PIV).
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Yasser Hussein. Analyse de champs de vitesse par FTLE à partir de la méthode des moments : validation théorique et expérimentale. Autre. ISAE-ENSMA Ecole Nationale Supérieure de Mécanique et d'Aérotechique - Poitiers, 2016. Français. ⟨NNT : 2016ESMA0009⟩. ⟨tel-01399055⟩

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