000002379 001__ 2379
000002379 005__ 20181220113750.0
000002379 022__ $$a1099-4300
000002379 0247_ $$2DOI$$a10.3390/e20020109
000002379 037__ $$aARTICLE
000002379 041__ $$aeng
000002379 245__ $$aTsallis extended thermodynamics applied to 2-d turbulence :$$bLévy statistics and q-fractional generalized kraichnanian energy and enstrophy spectra
000002379 260__ $$c2018
000002379 269__ $$a2018-02
000002379 300__ $$a41 pages
000002379 500__ $$aThis article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes
000002379 506__ $$avisible
000002379 520__ $$9eng$$aThe extended thermodynamics of Tsallis is reviewed in detail and applied to turbulence. It is based on a generalization of the exponential and logarithmic functions with a parameter q. By applying this nonequilibrium thermodynamics, the Boltzmann-Gibbs thermodynamic approach of Kraichnan to 2-d turbulence is generalized. This physical modeling implies fractional calculus methods, obeying anomalous diffusion, described by Lévy statistics with q < 5/3 (sub diffusion), q = 5/3 (normal or Brownian diffusion) and q > 5/3 (super diffusion). The generalized energy spectrum of Kraichnan, occurring at small wave numbers k, now reveals the more general and precise result k−q. This corresponds well for q = 5/3 with the Kolmogorov-Oboukov energy spectrum and for q > 5/3 to turbulence with intermittency. The enstrophy spectrum, occurring at large wave numbers k, leads to a k−3q power law, suggesting that large wave-number eddies are in thermodynamic equilibrium, which is characterized by q = 1, finally resulting in Kraichnan’s correct k −3 enstrophy spectrum. The theory reveals in a natural manner a generalized  temperature of turbulence, which in the non-equilibrium energy transfer domain decreases with wave number and shows an energy equipartition law with a constant generalized temperature in the equilibrium enstrophy transfer domain. The article contains numerous new results; some are stated in form of eight new (proven) propositions.
000002379 546__ $$aEnglish
000002379 540__ $$acorrect
000002379 592__ $$aHEIG-VD
000002379 592__ $$bIGT - Institut de Génie Thermique
000002379 592__ $$cIngénierie et Architecture
000002379 65017 $$aIngénierie
000002379 6531_ $$9eng$$aextended thermodynamics
000002379 6531_ $$9eng$$aTsallis entropy
000002379 6531_ $$9eng$$aescort probability
000002379 6531_ $$9eng$$afractional calculus
000002379 6531_ $$9eng$$a2-d turbulence
000002379 6531_ $$9eng$$aspectra of Kraichnan
000002379 6531_ $$9eng$$aKolmogorov-Oboukov spectrum
000002379 6531_ $$9eng$$aLévy statistics
000002379 6531_ $$9eng$$aintermittency
000002379 655__ $$ascientifique
000002379 700__ $$aEgolf, Peter William$$uHaute école d’ingénierie et de gestion du canton de Vaud (HEIG-VD) HES-SO // Haute Ecole Spécialisée de Suisse Occidentale
000002379 700__ $$aHutter, Kolumban$$uLaboratory of Hydraulics, Hydrology and Glaciology, Swiss Federal Institute of Technology, ETH
000002379 773__ $$g2018, 20(2), 109$$tEntropy
000002379 8564_ $$s2520408$$uhttps://hesso.tind.io/record/2379/files/Egolf_2018_Tsallis.pdf
000002379 8564_ $$s2466569$$uhttps://hesso.tind.io/record/2379/files/Egolf_2018_Tsallis.pdf?subformat=pdfa$$xpdfa
000002379 906__ $$aGREEN
000002379 909CO $$ooai:hesso.tind.io:2379$$pGLOBAL_SET
000002379 950__ $$aI2
000002379 980__ $$ascientifique