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