Stabilty of flow and introduction to turbulence

Lecturer(s): Christophe BAILLY, Andrea MAFFIOLI
Course ⋅ 20 hTC ⋅ 16 hAutonomy ⋅ 12 h


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).

Palabras clave

Laminar flow, linear stability, inviscid (Rayleigh) and viscous (Orr-Sommerfeld) approaches, turbulent signals, intermittency, entrainment, free shear flows


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

Learning Outcomes

  • Master the concepts of linear stability analysis of flows
  • Know how to characterize turbulent signals
  • Be more familiar with the phenomenology of turbulent flows
  • Know how to physically exploit the results of a stability analysis


Final mark = 50% Knowledge + 50% Know-how Knowledge mark = 50% final exam + 50% continuous assessment Know-how mark = 50% final exam + 50% continuous assessment