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 instability - basic concepts and some examples. Linear and non-linear stability. Linearization of the equations of motion. Method of normal modes. Instability threshold and critical modes. Kelvin-Helmholtz and Rayleigh-Bénard instability. Simple shear flows. 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.