My teaching in University Lille, ecole centrale and international master in turbulence

  1. Turbulence Lectures
  2. Mécanique des Milieux Continus (MMC)
  3. Numerical methods
  4. Fluids mechanics
  5. Finite Volume 
  6. Master Calcul Scientifique 



The course will provide students with an introduction to the fundamentals of turbulent flow. The focus will be on understanding the averaged equations of motion and the underlying physics they contain. The main goal will be to provide students with the tools necessary to continue the study of turbulence whether in a university or industrial setting. Topics covered will include: what turbulence is ; Reynolds-averaged equations; the origin of turbulence; simple closure models Reynolds stress equations; simple decaying turbulence; homogeneous shear flow turbulence; free turbulent shear flows; wall-bounded turbulent flows; multi-point and spectral considerations. Particular attention will be given to those processes which control the production and dissipation of turbulence energy. 

The concept of 'scale' will be explored in detail using probabilistic and spectral techniques. These techniques will be used to examine how energy is transferred from the mean flow to the turbulence, from one turbulence scale to another, and how energy is dissipated. Similarity ideas will be introduced as appropriate to illustrate how the various parts of the flow fit together and how they are affected by Reynolds number. The ideas and concepts discussed form the bulk of our understanding of turbulence as well as the current tools for advancing the state of our knowledge about it.

Throughout the course, the emphasis will be put on showing how such ideas affect engineering practice, experimental design and computer model development. The goal is not only to learn about current understanding but also to learn about where the problems are so that students can prepare for continuing to learn as new ideas and models develop. 



Part I : The turbulence facts

Part II : The governing equations

Part III : The statistical description of turbulence

Part IV : Turbulence modeling

Part V : Turbulent wall bounded flows 

Part VI : Homogeneous Isotropic Turbulence

Part VII : Homogeneous shear flows

Part VIII : Dynamics of 3D turbulent flows



Written examination 2016-02-09


  1. Vectors, tensors and the basic equations of fluid mechanics, Rutherford Aris, Dover.
  2. Turbulence : The legacy of A. N. Kolmogorov, U. Frisch, CUP.
  3. Turbulent Flows, S. Pope, CUP, 2000.
  4. A First Course in Turbulence By Henk Tennekes and John L. Lumley, MIT Press 1972.
  5. Turbulence in Fluids, M. Lesieur, Springer 2008.