2000/01/31 by Victor Yakhot, M.G. Snel · 1 citation
Business, Management and Accounting · Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · Physics and Astronomy · Psychology · Social Sciences · #Cognitive psychology #Communication #Consumer Behavior in Brand Consumption and Identification #Dissipation #Evolutionary Psychology and Human Behavior #Fluid Dynamics and Turbulent Flows #Gaussian #Geometry #Intermittency #Length scale #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Nonverbal communication #Persuasion #Physics #Psychology #Psychology of Social Influence #Quantum mechanics #Scaling #Social psychology #Statistical physics #Turbulence #Vector field #Wind and Air Flow Studies #nlin.CD
paper · pdf · doi:10.1103/physreve.63.026307
25 pages, 1 figure
arxiv created 2000/02/17 · arxiv updated 2009/11/30 · openalex publication_date 2010/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/28
Numerical and physical experiments on two-dimensional (2D) turbulence show that the differences of transverse components of velocity field are well described by Gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume the existence of a critical space dimensionality d=d(c), at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At d<d(c) the flow can be described by the "mean-field theory," leading to the observed Gaussian statistics and Kolmogorov scaling of transverse velocity differences. It is shown that in the vicinity of d=d(c) the ratio of the relaxation and translation characteristic times decreases to zero, thus giving rise to a small parameter of the theory. The expressions for pressure and dissipation contributions to the exact equation for the generating function of transverse velocity differences are derived in the vicinity of d=d(c). The resulting equation describes experimental data on two-dimensional turbulence and demonstrates the onset of intermittency as d-d(c)>0 and r/L-->0 in three-dimensional flows in close agreement with experimental data. In addition, some exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point probability density function of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a Gaussian.