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Advanced Fluid Mechanics: Transition to Turbulence & Turbulence - Applications to Transfers, Aerodynamics & Wind Energy

ECTS Credits: 3

Duration: 21 hours + 9 h Erasmus & Fondation

Semester: S9

Persons in charge:

Emmanuel Plaut, professor Uni. of Lorraine - 

Joachim Peinke, professor Uni. of Oldenburg -

Keywords: Nonlinear physics, instabilities, bifurcations, statistical and stochastic modeling, wind energy

Prerequisites: Statistics, Fluid mechanics


Introduction to the theory of bifurcations, in the context of the transition to spatio-temporal complexity or turbulence in fluid systems. Advanced turbulence modeling. Importance of small scale turbulence in the context of Wind Energy.


In the first part of this course (sessions 1-6), given by EP, the theory of bifurcations (or `catastrophe theory') is introduced. This theory is of general interest since it is relevant for many nonlinear systems, also, outside of the domain of Mechanics. Of course it is illustrated here with examples of fluid systems. The methodology of linear and weakly nonlinear stability analyses is presented and operated. In order to solve in an efficient manner the PDEs encountered, formal calculations and numerical computations with spectral methods are introduced and programmed with Mathematica. The examples studied are thermal convection, in a closed configuration, and aerodynamical waves in open flows (flows over a plate or an obstacle, in a channel, ...).

In the second part of this course (sessions 7-9), given by JP, statistical and stochastic modeling of turbulence is presented, focusing on the universal structure of small scale turbulence as well as on applications to Wind Energy. The small scale statistics of turbulent flows is reviewed: cascade, power spectra, intermittency corrections, extreme events... For Wind Energy, the characterization of wind conditions is presented: the IEC 61400 norm is described, and `wind gusts' are discussed. Experimental methods to investigate the impact of turbulence on the wind energy conversion, like sensors and wind tunnel with (active) grids, are presented. Finally, methods are developed, to handle the turbulent dynamical aspects of the energy conversion of a wind turbine. Topics are power output for a single turbine and a farm, as well as monitoring fatigue.

The last session corresponds to a test with programming, EP will help and validate one or more steps.

Web page of the module: .

A funding of the ERASMUS program and of the Fondation Mines Nancy permits the involvement of JP, who has been recently the president of the European Academy of Wind Energy.


Transition to Turbulence:

  • understand basic thermoconvection phenomena, in particular, the Rayleigh-Bénard system: onset through an instability and supercritical bifurcation, notion of secondary instabilities, ...
  • understand the fundamentals of the transition to turbulence in Open Shear Flows: subcritical bifurcation, strong secondary instabilities, ...
  • be able to perform, with some guidance, a linear stability analysis, either with formal calculations or a numerical spectral method
  • understand the bases of the weakly nonlinear analysis, up to the computation of amplitude equations; be able to perform such a weakly nonlinear analysis with some guidance

Wind Energy and Turbulence:

  • knowledge of quantities that characterize turbulence (turbulent energy, length scales, ...)
  • be able to extract from a velocity time series mean and standard deviation values, a PDF of the velocity and of the velocity increments, understand the notion of intermittency and extreme events
  • understand the importance of the wind speed characteristics for Wind Energy
  • be able to construct the IEC power curve from real data



  •  Written test
  • Continous assessment
  • Oral presentation
  • Project
  • Written report
  • Aucune étiquette