Tiziano Pagliaroli

Coherent Structures, Wavelet Analysis and Chaotic Dynamics in Fluid Mechanics

Fluid flows exhibit behaviours ranging from regular oscillations to strongly nonlinear, intermittent and chaotic dynamics. Understanding such phenomena requires mathematical tools capable of capturing both the dominant spatial organization of the flow and its evolution across multiple temporal scales.

This seminar will provide a general overview of the problem, with emphasis on the physical interpretation of complex fluid-dynamic behaviours and on selected techniques for data analysis. In particular, Proper Orthogonal Decomposition (POD) will be introduced as a powerful framework to extract the most energetic coherent structures and identify low-dimensional flow organizations. 

The seminar will finally address chaotic behaviours in fluid mechanics, highlighting how deterministic nonlinear systems may display sensitivity to initial conditions, irregular transitions and loss of predictability (see fig.3). Through few examples drawn from fluid-dynamic applications, the combined use of modal decomposition, wavelet transform and recurrence quantification analysis will be shown to provide an effective route for interpretation of complex numerical or experimental datasets, identifying physically relevant mechanisms.