The Kolmogorov Law of Turbulence What Can Rigorously Be Proved? Part II

  • Roger Lewandowski
  • Benoît PinierEmail author
Part of the Understanding Complex Systems book series (UCS)


We recall what are the different known solutions for the incompressible Navier-Stokes Equations, in order to fix a suitable functional setting for the probabilistic frame that we use to derive turbulence models, in particular to define the mean velocity and pressure fields, the Reynolds stress and eddy viscosities. Homogeneity and isotropy are discussed within this framework and we give a mathematical proof of the famous \(-5/3\) Kolmogorov law, which is discussed in a numerical simulation performed in a numerical box with a non trivial topography on the ground.

MCS Classification

76D05 76F65 65M60 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.IRMAR, UMR 6625Université Rennes 1, and Fluminance Team INRIARennes cedexFrance

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