Stabilty of flow and introduction to turbulence

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 - Stability of flows - basic notions and tools. Local and global instabilities. Instability thresholds and dimensionless parameters. Linearization. Parallel plane flows. Orr-Somerfeld equation. Non-viscous instabilities: Rayleigh equation. Piecewise linear profiles. Monotonic profiles and neutral modes. Effects of weak nonlinearities. - 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