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

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Book cover The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

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.

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Notes

  1. 1.

    k already denotes the TKE, and from now also the wavenumber, k =  | k | . This is commonly used in turbulence modeling, although it might sometimes be confusing.

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Authors and Affiliations

  1. IRMAR, UMR 6625, Université Rennes 1, and Fluminance Team INRIA, Campus Beaulieu, 35042, Rennes cedex, France

    Roger Lewandowski & Benoît Pinier

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  1. Roger Lewandowski
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  2. Benoît Pinier
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Correspondence to Benoît Pinier .

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  1. ManLab Technical University of Crete, Chania, Greece

    Christos Skiadas

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Lewandowski, R., Pinier, B. (2016). The Kolmogorov Law of Turbulence What Can Rigorously Be Proved? Part II. In: Skiadas, C. (eds) The Foundations of Chaos Revisited: From Poincaré to Recent Advancements. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-29701-9_5

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