On distributions of velocity random fields in turbulent flows
Abstract
The purpose of the present paper is to derive a partial differential equation (PDE) for the singletime singlepoint probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly nonlinear parabolictransport equation, which depends on two conditional statistical numerics of important physical significance. The PDF PDE is a general form of the classical Reynolds mean flow equation, and is a precise formulation of the PDF transport equation. The PDF PDE provides us with a new method for modelling turbulence. An explicit example is constructed, though the example is seemingly artificial, but it demonstrates the PDF method based on the new PDF PDE.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.03219
 Bibcode:
 2021arXiv210703219L
 Keywords:

 Mathematical Physics;
 Physics  Fluid Dynamics;
 35D40;
 35K65;
 76D05;
 76D06;
 76F05;
 76M35
 EPrint:
 3 figures