1994/10/20 by В. В. Лебедев, Lebedev, Vladimir V., Victor S. L’vov +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.chao-dyn/9410003
openalex publication_date 1994/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that statistical properties of developed hydrodynamic turbulence are characterized by an infinite set of independent anomalous exponents which describes the scaling behavior of hydrodynamic fields constructed from the second and larger powers of the velocity derivatives. A physical mechanism responsible for anomalous scaling, ``telescopic multi-step eddy interaction", is discovered and investigated. The essence of this mechanism is the existence of a very large number (R/η)Δj≫ 1 of channels of interaction of large eddies of scale R in the inertial interval with eddies of viscous scale η via a set of eddies of all intermediate scales between R and η. The description of this mechanism based on the NS equation in the quasi Lagrangian representation is presented. In the diagrammatic expansion of the correlation function of the energy dissipation field K_ ε ε(R), we have found an infinite series of logarithmically diverging diagrams. Their summation leads to a renormalization of the normal Kolmogorov-41 dimensions. For a description of the scaling of various hydrodynamic fields an infinite set of primary fields On with independent scaling exponents Δn was introduced. We have proposed a symmetry classification of the fields On enabling one to predict relations between scaling the behavior of different correlation functions.