Analysis of fully developed turbulence in terms of Tsallis statistics

Abstract

The analysis of the fully developed turbulence with the help of the binomial multiplicative process is reinvestigated from the standpoint of Tsallis nonextensive statistics in order to provide some insight in understanding the underlying physical meaning of the Tsallis ensemble. The formula is derived which relates Tsallis index q with the intermittency exponent that is a manifestation of multifractality of the sizes of eddies. It is shown that the probability density function of the local dissipation of turbulent kinetic energy can be represented by a distribution function of the type in Tsallis statistics with the index q determined by the experimentally observable quantity through the derived formula.

Escape time in anomalous diffusive media

“…(2) have the form of the Maximum Tsallis Entropy probability distributions, as already discussed previously [15][16][17], even in the absence of external drift [14,18]. It is worth recalling that phemonena such as full developed turbulence [19], the hadronic transverse moment distribution in high energy scattering process e + e − → hadrons [20], among others, have been satisfactorily described in terms of distributions similar to (3) instead of the canonical stationary one. Steady state solutions are illustrated in Fig.…”

Nonextensive statistical mechanics: a brief review of its present status

“…Ramos et al advanced in 1999 [10] the possibility of nonextensive statistical mechanics being useful for such systems. The idea was since then further developed by Beck [11] and by the Arimitsu's [12], basically simultaneous and independently. They proposed theories within which the probability distribution of the velocity differences and related quantities are deduced from basic considerations.…”

“…In particular, a natural arena for this statistical mechanics appears to be the so called complex systems [9]. We shall briefly review here four recent applications, namely fully developed turbulence [10][11][12], hadronic jets produced by electron-positron annihilation [13], motion of Hydra viridissima [14], and quantitative linguistics [15].…”

Entropy Generation through a Deterministic Boundary-Layer Structure in Warm Dense Plasma

“…We have also found that the empirical modes obtained from the singular value decomposition indicate empirical entropic indices. We will therefore, heuristically, apply a relationship, found by Arimitsu and Arimitsu [27], between the entropic index of Tsallis and the intermittency exponent required to account for the fractal nature of turbulent energy dissipation. We will substitute the absolute value of the empirical entropic index discussed in the previous section into the original derivation by Arimitsu and Arimitsu [27].…”

“…In Section 8, the empirical entropic index (Tsallis [24]) is computed from the empirical entropy value for each empirical mode ( [11,20], Mariz [25], Glansdorff and Prigogine [26]). Section 9 presents the intermittency exponent (Arimitsu and Arimitsu [27], Mathieu and Scott [28]) from the associated empirical entropic index for each empirical mode of the singular value decomposition process (Press et al [29], Isaacson [31]). Section 10 presents the calculation of the entropy generation rate (de Groot and Mazur [34], Truitt [35], Bejan [36]) through the dissipation of the appropriate part of the total kinetic energy applied as input to the original deterministic structures produced within the three-dimensional boundary layer environment (Fung and Vassilicos [37], Hurst and Vassilicos [38], Seoud and Vassilicos [39], Mazellier and Vassilicos [40] and Valente and Vassilicos [41]).…”