Abstract
In 1941 Kolmogorov and Obukhov [9, 12] proposed that there exists a statistical theory of turbulence that should allow the computation of all the statistical quantities that can be computed and measured in turbulent systems. These are quantities such as the moments, the structure functions and the probability density functions (PDFs) of the turbulent velocity field. The Kolmogorov-Obukhov ’41 theory predicted that the structure functions of turbulence, that are the moments of the velocity differences at distances separated by a lag variable l, should scale with the lag variable to a power p/3 for the pth structure function, multiplied by a universal constant.
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References
Barndorff-Nilsen, O.E.: Exponentially decreasing distributions for the logarithm of the particle size. Proc. R. Soc. London A353, 401–419 (1977)
Barndorff-Nilsen, O.E., Blaesild, P., Schmiegel, J.: A parsimonious and universal description of turbulent velocity increments. Eur. Phys. J. B 41, 345–363 (2004)
Bernard, P.S., Wallace, J.M.: Turbulent Flow. John Wiley & Sons, Hoboken (2002)
Birnir, B.: Turbulence of a unidirectional flow. In: Proceedings of the Conference on Probability, Geometry and Integrable Systems, MSRI, p. 55. MSRI Publications, Cambridge Univ. Press (December 2007), http://repositories.cdlib.org/cnls/
Birnir, B.: The Kolmogorov-Obukhov statistical theory of turbulence. J. Nonlinear Sci. (2013), doi:10.1007/s00332-012-9164-z
Birnir, B.: The Kolmogorov-Obukhov Theory of Turbulence. Springer, New York (2013)
Dubrulle, B.: Intermittency in fully developed turbulence: in log-Poisson statistics and generalized scale covariance. Phys. Rev. Letters 73(7), 959–962 (1994)
Hopf, E.: Statistical hydrodynamics and functional calculus. J. Rat. Mech. Anal. 1(1), 87–123 (1953)
Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 9–13 (1941)
Kolmogorov, A.N.: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85 (1962)
Leray, J.: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63(3), 193–248 (1934)
Obukhov, A.M.: On the distribution of energy in the spectrum of turbulent flow. Dokl. Akad. Nauk SSSR 32, 19 (1941)
Obukhov, A.M.: Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81 (1962)
Reynolds, O.: An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the the law of resistance in parallel channels. Phil. Trans. Roy. Soc. Lond. 174(11), 935–982 (1883)
Reynolds, O.: On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Roy. Soc. Lond. 186A, 123–164 (1885)
She, Z.-S., Leveque, E.: Universal scaling laws in fully developed turbulence. Phys. Rev. Letters 72(3), 336–339 (1994)
She, Z.-S., Waymire, E.: Quantized energy cascade and log-poisson statistics in fully developed turbulence. Phys. Rev. Letters 74(2), 262–265 (1995)
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Birnir, B. (2014). The KOSL Scaling, Invariant Measure and PDF of Turbulence. In: Talamelli, A., Oberlack, M., Peinke, J. (eds) Progress in Turbulence V. Springer Proceedings in Physics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-01860-7_5
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DOI: https://doi.org/10.1007/978-3-319-01860-7_5
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