On the initial conditions of the 1-point PDF for incompressible Navier-Stokes fluids

Details On the initial conditions of the 1-point PDF for incompressible Navier-Stokes fluids On the initial conditions of the 1-point PDF for incompressible Navier-Stokes fluids

2010-03-07

arxiv.org/abs/1003.1474v1

Physics

Fluid Dynamics

Scientific paper

An aspect of fluid dynamics lies in the search of possible statistical models for Navier-Stokes (NS) fluids described by classical solutions of the incompressible Navier-Stokes equations (INSE). This refers in particular to statistical models based on the so-called inverse kinetic theory (IKT) . This approach allows the description of fluid systems by means a suitable 1-point velocity probability density function (PDF) which determines, in terms of suitable "moments", the complete set of fluid fields which define the fluid state. A fundamental related issue lies in the problem of the unique construction of the initial PDF. The goal of this paper is to propose a solution holding for NS fluids. Our claim is that the initial PDF can be uniquely determined by imposing a suitable set of physical realizability constraints.

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