### Current browse context:

math-ph

### Change to browse by:

### References & Citations

# Mathematical Physics

# Title: On distributions of velocity random fields in turbulent flows

(Submitted on 7 Jul 2021)

Abstract: The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear parabolic-transport 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.

Link back to: arXiv, form interface, contact.