Ab initio construction of the 2-point velocity difference PDF for incompressible Navier-Stokes fluids
Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127, Trieste, Italy
2 Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601, Opava, Czech Republic
Revised: 2 June 2013
Accepted: 14 July 2013
Published online: 5 August 2013
Characterizing hydrodynamic turbulence in terms of the so-called 2-point velocity difference statistics is a basic aspect of fluid dynamics, both from the theoretical and experimental viewpoints. The issue concerns in particular the first-principle construction of the corresponding 2-point velocity difference probability density function (PDF) as well as the transport equation which determines its time evolution. The goal of this paper is to point out that the problem can be solved by suitably prescribing the ensemble-averaging operator to be employed in the statistical description of fluids. As a result, qualitative properties of the 2-point PDF which are usually ascribed to the occurrence of turbulence are shown to follow from the ab initio approach presented here and to characterize both deterministic and stochastic fluid descriptions.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2013