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Entropy 2015, 17(4), 2198-2217; doi:10.3390/e17042198

Entropic-Skins Geometry to Describe Wall Turbulence Intermittency

1
Laboratory Energetics Mechanics Electromagnetism (LEME), Université Paris Ouest Nanterre la Défense, Pôle de Ville d'Avray, 50 rue de Sèvres 92410 Ville d'Avray, France
2
IRSTEAF, 17 Avenue de Cucillé CS 64429-35044 Rennes Cedex, France
3
Ecole Centrale de Lille, LML UMR 8107, Bv Paul Langevin, 59655 Villeneuve d'Ascq Cedex, France
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 28 January 2015 / Revised: 30 March 2015 / Accepted: 31 March 2015 / Published: 13 April 2015
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Abstract

In order to describe the phenomenon of intermittency in wall turbulence and, more particularly, the behaviour of moments and and intermittency exponents ζP with the order p and distance to the wall, we developed a new geometrical framework called “entropic-skins geometry” based on the notion of scale-entropy which is here applied to an experimental database of boundary layer flows. Each moment has its own spatial multi-scale support Ωp (“skin”). The model assumes the existence of a hierarchy of multi-scale sets Ωp ranged from the “bulk” to the “crest”. The crest noted characterizes the geometrical support where the most intermittent (the highest) fluctuations in energy dissipation occur; the bulk is the geometrical support for the whole range of fluctuations. The model assumes then the existence of a dynamical flux through the hierarchy of skins. The specific case where skins display a fractal structure is investigated. Bulk fractal dimension and crest dimension are linked by a scale-entropy flux defining a reversibility efficiency (d is the embedding dimension). The model, initially developed for homogeneous and isotropic turbulent flows, is applied here to wall bounded turbulence where intermittency exponents are measured by extended self-similarity. We obtained for intermittency exponents the analytical expression with γ ≈ 0.36 in agreement with experimental results. View Full-Text
Keywords: turbulence; wall turbulence; intermittency; fractals; entropic-skins geometry; scale-entropy turbulence; wall turbulence; intermittency; fractals; entropic-skins geometry; scale-entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Queiros-Conde, D.; Carlier, J.; Grosu, L.; Stanislas, M. Entropic-Skins Geometry to Describe Wall Turbulence Intermittency. Entropy 2015, 17, 2198-2217.

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