Ense3 rubrique Formation 2022

Applied Fluid Mechanics for the Environment - 4EUS3MFE

  • Number of hours

    • Lectures 25.0
    • Projects -
    • Tutorials 25.0
    • Internship -
    • Laboratory works 10.0
    • Written tests 0


    ECTS 5.0


The course is composed in three parts :
- turbulence: physical and modelling aspects
- diffusion and dispersion in the Environment
- environmental fluid mechanics


Olivier METAIS


Turbulence: physical and modelling aspects(12 h of lecture and 4h of supervised work)
o Turbulent flows characteristics
o Statistical approach : averaging, Reynolds equations ; turbulent eddy-viscosity and diffusivity ; turbulent boundary layer ; energy mechanisms: production and dissipation
o Statistical tools and theories : correlations ; Fourier space ; kinetic energy and dissipation spectra ; turbulent scales ; Kolmogorov theory
o Turbulent shear flows : example of the plane jet
o The different approaches for turbulence modelling and simulation: statistical modelling, direct numerical simulation, large eddy simulation
o Statistical modelling: concept of order ; zero, one and two-equations models ;
k-epsilon model; second order model
o Large-eddy simulation : methodology ; Smagorinsky model

Diffusion and dispersion in the Environment (6 h of lecture et 2h of supervised work)
Content :
o Diffusion concept and Fick’s law : diffusion equation ; molecular and turbulent diffusion coefficients
o Unidirectional diffusion problem : concentrated injection ; extended injection ; presence of walls ; diffusion in a current
o Multidirectional diffusion problems : concept of plume
o Dispersion in shear flows : longitudinal dispersion coefficient
o Application to turbulent flows in rivers : characteristic turbulent velocity and velocity profile ; mixing distances in rivers ; flow rate determination
o Diffusion in fully-developed turbulence: diffusion of a cloud of tracers ; particle dispersion ; dispersion of particles ; Taylor’s theorem ; Richardson law .

Environmental fluid mechanics (12h of lecture et 12h of supervised work)
Content :

  • Dimensional analysis and Vashy-Buckingham theorem
  • Laminar boundary layer : Blasius equation and resolution methods ; boundary layer with adverse pressure gradient and separation
  • Energy equation ; Equation de l’énergie ; Compressible flow statics and concept of atmospheric stability
  • Rotating flows ; centrifugal and Coriolis forces ; Ekman layer
  • Vorticity dynamics
    12h of practical activities


Basis in Fluid mechanics


Session normale / First session
Evaluation non rattrapable (EN) / EN assessment
Evaluation rattrapable (ER) / ER assessment : épreuve écrite de 4h / 4h written exam

Session de rattrapage / Second session
La note remplace la note de ER. Le EN n'est pas rattrapable. / Written or oral exam will replace the first one (ER). No retake for EN.

EN*1/3 + ER*2/3


The course exists in the following branches:

see the course schedule for 2023-2024

Additional Information

Course ID : 4EUS3MFE
Course language(s): FR

You can find this course among all other courses.