The Essentials of Linear and Nonlinear Theories and Models

  • Pierre Sagaut
  • Claude Cambon


This chapter gathers elements from linear theory and from nonlinear closures, addressed in two different chapters in the previous edition. Complements to Rapid Distortion Theory, now anticipated in Chap.  2 and given in Chap.  8 for strictly homogeneous turbulence, are given until its general extension using WKB approximation. Quasi-linear variants of ray methods with and without propagating waves are introduced. Then, nonlinear closures, essentially triadic, are revisited, with complete equations for all variants of EDQNM and wave turbulence for purely rotating turbulence. Detailed equations of the model in the presence of any mean velocity gradients, simplified in terms of spherically averaged descriptors (and used in both chaps.   8 and  9) are given.


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© Springer International Publishing AG, part of Springer Nature 2018

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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