Entropic-Skins Geometry to Describe Wall Turbulence Intermittency

In order to describe the phenomenon of intermittency in wall turbulence and, more particularly, the behaviour of moments p r V δ and p r ε 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 f Δ and crest dimension ∞ Δ are linked by a scale-entropy flux defining a reversibility efficiency ( ) / ( ) f d γ ∞ ∞ = Δ −Δ −Δ (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 OPEN ACCESS Entropy 2015, 17 2199 self-similarity. We obtained for intermittency exponents the analytical expression [ ] /3 ( (1 ) 3 2) / 3 (3 )(1 ) p p p ζ γ γ γ ∞ ∞ = Δ − + − + −Δ − with γ ≈ 0.36 in agreement with experimental results.