Governing Equations, from Dynamics to Statistics

  • Pierre Sagaut
  • Claude Cambon


This chapter provides an exhaustive presentation of governing equations for continuum fluid mechanics, along with main tools for turbulent flow analysis and modeling: statistical averaging, anisotropy description, Fourier space analysis and modal decomposition of turbulent motion. The use of Green functions to solve linear and nonlinear problems is also discussed, along with the general treatment of governing equations in a Lagrangian framework. Splitting of the solution in compressible flows via Helmholtz decomposition is presented. The optimal reference frame in Fourier space based on Craya’s decomposition, including helical mode decomposition, is extensively discussed. An introduction to turbulence modelling is given.


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Authors and Affiliations

  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres, UMR CNRS 7340, Ecole Centrale de MarseilleAix-Marseille UniversitéMarseilleFrance
  2. 2.Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509Ecole Centrale de LyonÉcullyFrance

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