Physics of turbulent flows

Lecturer(s): Christophe BAILLY, Christophe BOGEY, Marc JACOB
Course ⋅ 16 hPW ⋅ 8 hStudy ⋅ 4 h


The course introduces different aspects of the physics of turbulent flows and associated modeling, and illustrates in a practical way some recent results from experimental and numerical studies. The main objectives are to master the basic concepts (generation/development of turbulence, turbulence boundary layer, local equilibrium, non-local role of vorticity, homogeneous and isotropic turbulence, Kolmogorov theory), to develop skills in turbulence modelling and in the analysis of results, as well as to provide an overview of experimental approaches.


Turbulence, Reynolds number, turbulent boundary layer, vorticity dynamics, energy transfers, homogeneous and isotropic turbulence, Kolmogorov's theory


  1. Some general properties of turbulence, turbulent structure in spectral space, scales, time average and ergodicity; 2. Mean flow field: Reynolds decomposition, kinetic energy budget, closure by turbulent viscosity, examples and consequences; 3. Wall-bounded turbulent flows: log-law, closure models, phenomenology; 4 - Vorticity:definition, Biot & Savart, deformation, Helmholtz Eq., rapid distorsion theory, vortex pairing, enstrophy, helicicity; 5. Homogeneous and isotropic turbulence: two-point velocity correlation tensor, length scales, spectral tensor, isotropic, 1-D spectra, Taylor's assumption, energy spectrum, isotropic turbulence, Karman & Howarth relation, experiments, Kolmogorov's theory, Lin's eq.; 6. Flow field survey and visualization

Learning Outcomes

  • Know the spatio-temporal description of turbulence
  • Be able to describe and model some classical turbulent flows
  • Know how to interpret the behavior of turbulent flows


Final mark = 50% Knowledge + 50% Know-how Knowledge = 80% homework assignements + 20% lab work Know-how = 40% homework assignements + 60% lab work

For students involved in a MSc, there is an additional final exam (closed book and open notes), the final mark for the MSc is calculated by 50% final exam + 30% homework assignements + 20% lab work