Fluid Flow Data Processing and Visualization

This course is a general introduction to data processing techniques used in fluid mechanics to analyse unsteady flows. Specifically, techniques related to the flow visualization and the postprocessing of numerical data will be presented. The overall content of the course is:

1. Review of fundamentals of turbulent flows (energy cascade, Reynolds-averaged equations, Reynolds stress, turbulent kinetic energy, vorticity equation, turbulence spectrum, energy budget, ...)

2. Characteristics of flow datasets (Nyquist criterion, sampling and resolution, first principle of visualization, vortex/Q criteria, ...)

3. Statistical analysis in flows

- Deterministic/random data

- Averaging (ensemble, condition, phase)

- Probability: PDFs, statistical moments, conditional PDFs

- Correlation function

- Ergodic hypothesis

- Statistical convergence and uncertainty

4. Temporal and spectral data processing

- Fourier transform

- Physical/spectral space and multi-dimensional FFTs

- Auto/cross spectra

- Integral length/time scale

- Convolution (filtering) and transfer function

5. Modal analysis and coherent structure eduction

- Proper Orthogonal Decomposition

- Dynamic Mode Decomposition

- Basics of reduced-order modelling