Due to the COVID19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
Teacher(s)
Language
English
Main themes
Starting from generalities on turbulence (problematics, turbulent channel flow or pipe flows, turbulent boundary layers, basic models), the course will present a detailed analysis of turbulence physics for diverse classes of canonical flows (homogeneous isotropic turbulence, free shear flows, wallbounded shear flows). The principal methods of numerical simulation (RANS and LES) will be presented. Diverse applications will be considered (industrial flows, aerodynamics, atmosphere, oceans).
Aims
At the end of this learning unit, the student is able to :  
1 
In consideration of the reference table AA of the program "Masters degree in Mechanical Engineering", this course contributes to the development, to the acquisition and to the evaluation of the following experiences of learning:

Content
Introduction and generalities: Turbulent flows, physics and characteristics of turbulence. Reynolds averages (temporal averages, ensemble averages), conservation equations for the mean fields, Reynolds stresses and fluxes: turbulent transfer or momentum, heat, mass. Linear models of effective turbulence viscosity and conductivity.
Turbulent shear flows with walls: Turbulent channel flows or pipe flows, turbulent boundary layers, characteristic lengths, friction velocity, frictionconduction temperature, turbulence effective viscosity and conductivity. Profiles: inner zone (near wall) including a laminar sublayer, buffer zone with logarithmic profile (von Karman), outer zone with composite profile (Coles). Effect of wall roughness.
Homogeneous isotropic turbulence (HIT): Large scales, inertial scales and small scales (Kolmogorov scale), spectral analysis, energy spectrum, energy cascade, Kolmogorov theory, Pao model spectrum, structure functions, twopoints correlations, Taylor microscales. Numerical simulation of HIT, and comparison with theory and with experimental results.
Turbulent free shear flows: jets and shear layers: Phenomenological description and visualization, coherent structures in turbulence, experimental and numerical simulation results (growth rate, effective turbulence viscosity), similarity analysis and similarity profiles.
Rotation and stratification effects: Turbulence in the presence of volume forces. Atmospheric and oceanic variability, geohydrodynamic equations, Ekman layers, energetics of turbulence in a stratified medium (stable or unstable), atmospheric and oceanic boundary layers. Environmental problems.
Natural convection: Thermal effects in turbulence. Scales in natural convection, Boussinesq approximation, conservation of energy. Atmospheric and oceanic convection.
Reynoldsaveraged approach(RANS, Reynolds Averaged NavierStokes equations): Conservation equations for the averaged fields and classical effective viscosity and conductivity models. Equation for the turbulent kinetic energy, k. Closure using one or two equations (mixing length model, kepsilon model, komega model). Calibration (using HIT and wallbounded turbulence). Stratification effect, and MellorYamada model. Boundary conditions.
Large eddy simulation (LES) approach: Truncation of physical scales and thus of the spectrum, resolved scales and subgrid scales. Truncated conservation equations and effective subgridscales stresses and heat fluxes. Smagorinsky model and his calibration in HIT. Recent developments and multiscale models. LES of wallbounded flows. Examples of applications. LES with explicit filtering added to the truncation (filtered and truncated fields).
Turbulent shear flows with walls: Turbulent channel flows or pipe flows, turbulent boundary layers, characteristic lengths, friction velocity, frictionconduction temperature, turbulence effective viscosity and conductivity. Profiles: inner zone (near wall) including a laminar sublayer, buffer zone with logarithmic profile (von Karman), outer zone with composite profile (Coles). Effect of wall roughness.
Homogeneous isotropic turbulence (HIT): Large scales, inertial scales and small scales (Kolmogorov scale), spectral analysis, energy spectrum, energy cascade, Kolmogorov theory, Pao model spectrum, structure functions, twopoints correlations, Taylor microscales. Numerical simulation of HIT, and comparison with theory and with experimental results.
Turbulent free shear flows: jets and shear layers: Phenomenological description and visualization, coherent structures in turbulence, experimental and numerical simulation results (growth rate, effective turbulence viscosity), similarity analysis and similarity profiles.
Rotation and stratification effects: Turbulence in the presence of volume forces. Atmospheric and oceanic variability, geohydrodynamic equations, Ekman layers, energetics of turbulence in a stratified medium (stable or unstable), atmospheric and oceanic boundary layers. Environmental problems.
Natural convection: Thermal effects in turbulence. Scales in natural convection, Boussinesq approximation, conservation of energy. Atmospheric and oceanic convection.
Reynoldsaveraged approach(RANS, Reynolds Averaged NavierStokes equations): Conservation equations for the averaged fields and classical effective viscosity and conductivity models. Equation for the turbulent kinetic energy, k. Closure using one or two equations (mixing length model, kepsilon model, komega model). Calibration (using HIT and wallbounded turbulence). Stratification effect, and MellorYamada model. Boundary conditions.
Large eddy simulation (LES) approach: Truncation of physical scales and thus of the spectrum, resolved scales and subgrid scales. Truncated conservation equations and effective subgridscales stresses and heat fluxes. Smagorinsky model and his calibration in HIT. Recent developments and multiscale models. LES of wallbounded flows. Examples of applications. LES with explicit filtering added to the truncation (filtered and truncated fields).
Teaching methods
Due to the COVID19 crisis, the information in this section is particularly likely to change.
Typically 13 courses in class, sessions of exercices in class, homeworks, an un project.
Evaluation methods
Due to the COVID19 crisis, the information in this section is particularly likely to change.
Evaluation of the reports of the homeworks and of the project, and written exam (possibly with an oral discussion about the homeworks or the project, or about a prepared question)
Online resources
Bibliography
 Lecture notes, slides and computer animations available on Moodle
 Tennekes H. and Lumley J. L., A First Course in Turbulence, The MIT Press, 1972
 Pope S. B., Turbulent Flows, Cambridge University Press (conseillé)
 Burchard H., Applied Turbulence Modelling in Marine Water, Springer Verlag
 CushmanRoisin B. and J.M. Beckers, Introduction to Geophysical Fluid Dynamics, Academic Press, 2011
 Transparents et documentation/notes complémentaires des titulaires.
Teaching materials
 Lecture notes, slides and computer animations available on Moodle
Faculty or entity
Force majeure
Teaching methods
When the sanitary situation no longers allows for physical presence, the lectures and exercice sessions are given remotely.
Evaluation methods
The written individual exam and the oral discussion are organized remotely.