Entropic-Skins Geometry to Describe Wall Turbulence Intermittency

Abstract

Abstract:In order to describe the phenomenon of intermittency in wall turbulence and, more particularly, the behaviour of moments 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 ( )/( )

Fractal Geometric Model for Statistical Intermittency Phenomenon

“…One of these models, the entropic skin geometry (E.S.G. ), shown to be in agreement with other experiments [17,48], is an interpretation of this intermittency phenomenon achieved through a coupling between the multiscale fractal geometry and statistical intermittent analysis within the turbulence by assuming the existence of a certain hierarchy of correlated fractal structures, characterizing the dynamics of fluctuation levels (skins). Each fluctuation level of the order p has been associated with a fluctuating field Ω p , representing a structure of dimension ∆ p , included in the field Ω p−dp of dimension ∆ p−dp , such as Ω p−dp ⊃ Ω p with ∆ p−dp < ∆ p .…”

“…In the statistical approach, the value of a structure function < ε(r) p > is given by its "active part", offering two contributions; the first one − ε(r) p is the average energy dissipation rate over the actual active part of the field, and the second f p (r) is the volume fraction, which indicates an intermittency factor and allows for the "lacunary aspect" of energy dissipation [3,20]. Thus, we would have:…”

“…Kolmogorov's theory in developed turbulence (K41) assumes that turbulence is statistically homogeneous (invariant due to spatial translation, far from limits), isotropic (invariant due to rotation), self-similar (invariant due to scale expansion) and stationary (invariant due to time translation) [1][2][3]. According to Kolmogorov's theory, the developed turbulence can be described using the structure functions of dissipated energy < ε(r) p > and velocity < ∆V(r) p >, with ε(r) the rate of energy dissipation per unit mass averaging over an r-dimensional ball and ∆V(r) the velocity fluctuation V between two points separated by a distance of r.…”

A scale-entropy diffusion equation to explore scale-dependent fractality

“…The scale-entropy diffusion equation (hereafter SED equation) permits to quantify the properties of multi-scale phenomena through scale-space [6] and has been applied mostly to describe turbulence [11] turbulent combustion [12] and sprays [13]. The scale-entropy (S) represents an evolutive potential, which is traduced by the capacity to fill the space of a phenomenon (the higher the scale-entropy, the less the phenomenon is disorganized).…”

An exergetic approach for materials fatigue

“…and Where are the fractal support and its location? The field of fractals in materials is well documented (Carpinteri, 1994;Hähner et al, 1998) and the reflections about fractal geometry (Mandelbrot, 1975;Le Méhauté et al, 1998), entropy minimisation and constructal theory (Bejan, 2006;Wechsatol et al, 2004) and geometrical structure of entropy generation (Queiros-Condé, 2003;Queiros-Condé et al, 2015a, 2015bCanivet et al, 2016) lead us to the exergy equation for a better understanding of mechanical fatigue.…”