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arXiv · 2107.03219

On distributions of velocity random fields in turbulent flows

Jiawei Li·Zhongmin Qian·Mingrui Zhou
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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.

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Jiawei Li, Zhongmin Qian, Mingrui Zhou. 2021-07-07. On distributions of velocity random fields in turbulent flows. https://arxiv.org/abs/2107.03219

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