1995/02/01 by Victor S. L’vov, L'vov, Victor, Itamar Procaccia +1
Engineering · Environmental Science · #Chaotic Dynamics (nlin.CD) #Combustion and flame dynamics #Condensed Matter (cond-mat) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.chao-dyn/9502010
openalex publication_date 1995/02/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The lectures presented by one of us (IP) at the Les Houches summer school\ndealt with the scaling properties of high Reynolds number turbulence in fluid\nflows. The results presented are available in the literature and there is no\nreal need to reproduce them here. Quite on the contrary, some of the basic\ntools of the field and theoretical techniques are not available in a\npedagogical format, and it seems worthwhile to present them here for the\nbenefit of the interested student. We begin with a detailed exposition of the\nnaive perturbation theory for the ensemble averages of hydrodynamic observables\n(the mean velocity, the response functions and the correlation functions). The\neffective expansion parameter in such a theory is the Reynolds number (Re); one\nneeds therefore to perform infinite resummations to change the effective\nexpansion parameter. We present in detail the Dyson-Wyld line resummation which\nallows one to dress the propagators, and to change the effective expansion\nparameter from Re to O(1). Next we develop the ``dressed vertex" representation\nof the diagrammatic series. Lastly we discuss in full detail the path-integral\nformulation of the statistical theory of turbulence, and show that it is\nequivalent order by order to the Dyson-Wyld theory. On the basis of the\nmaterial presented here one can proceed smoothly to read the recent\ndevelopments in this field.\n