2009/10/01 by Massimo Tessarotto, M. Tessarotto, Tessarotto, M. +3
Chemical Engineering · Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Rheology and Fluid Dynamics Studies #physics.class-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0910.0123
arxiv created 2009/10/01 · openalex publication_date 2009/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fundamental aspects of fluid dynamics are related to construction of statistical models for incompressible Navier-Stokes fluids. The latter can be considered either deterministic or stochastic, respectively for regular or turbulent flows. In this work we claim that a possible statistical formulation of this type can be achieved by means of the 1-point (local) velocity-space probability density function (PDF, f1) to be determined in the framework of the so-called inverse kinetic theory (IKT). There are several important consequences of the theory. These include, in particular, the characterization of the initial PDF [for the statistical model f1,Γ ] . This is found to be generally non-Gaussian PDF, even in the case of flows which are regular at the initial time. Moreover, both for regular and turbulent flows, its time evolution is provided by a Liouville equation, while the corresponding Liouville operator is found to depend only on a finite number of velocity moments of the same PDF. Hence, its time evolution depends (functionally) solely on the same PDF. In addition, the statistical model here developed determines uniquely both the initial condition and the time evolution of f1. As a basic implication, the theory allows the exact construction of the corresponding statistical equation for the stochastic-averaged PDFand the unique representation of the multi-point PDF's in solely in terms of the 1-point PDF. As an example, the case of the reduced 2-point PDF's, usually adopted for the statistical description of NS turbulence, is considered.