2010/03/09 by Claudio Asci, C. Asci, Asci, C. +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1003.1784
arxiv created 2010/03/09 · openalex publication_date 2010/03/09 · arxiv updated 2010/03/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
An open problem arising in the statistical description of turbulence is related to the theoretical prediction based on first principles of the so-called multi-point velocity probability density functions (PDFs) characterizing a Navier-Stokes fluid. In this paper it will be shown that - based on a suitable axiomatic approach - a solution to this problem can actually be achieved based on the so-called inverse kinetic theory (IKT), recently developed for incompressible fluids. More precisely, we intend to show, based on the requirement that the Boltzmann-Shannon entropy for the s-point velocity PDF (fs) is independent of the order s and is also maximal at all times, that all multi-point PDFs are necessarily factorized in terms of the corresponding 1-point velocity PDF (f1). As a consequence the multi-point PDFs usually considered for the phenomenological description of turbulence can be theoretically predicted \textitbased on the knowledge of % f1 achieved by means of IKT.