The turbulent state is encountered in industrial processes, in the atmosphere and the ocean for geophysical flows, as well as in biological fluids, to mention only a few examples. The first objective of this course is to present the analytical tools to characterize stability of flow, by considering small perturbations around a basic flow. The second part is an introduction to turbulence for free shear flows such as mixing layers, jets and wakes (intermittency, entrainment, fully developed flow).
General introduction - Flow stability - basic notions and tools. Local and global instabilities. Instability thresholds and dimensionless parameters. Linearization. Simple shear flows. Method of normal modes. Kelvin-Helmholtz instability and convective (Rayleigh-Bénard) instability. Inviscid stability analysis: Rayleigh equation. Piecewise linear profiles. - Turbulent flows - transition to turbulence, analysis of turbulent flow signals, general equations of turbulent flows; turbulent flows with free edges: intermittency, entrainment, identification of turbulent structures