Statistical Model of a Self-Similar Turbulent Plane Shear Layer

Abstract

A turbulence probability density function (pdf) equation model is employed to solve a self-similar turbulent plane shear layer. The proper similarity variable was introduced into the problem of interest to reduce the pdf equation into a spatially one-dimensional equation, which is still three dimensional in velocity space. Then the approximate moment method is employed to solve this simplified pdf equation. By the solutions of this equation, the various one-point mean quantities are immediatelly available. Agreement of the calculated mean velocity, turbulent energy and Reynolds stress with the available experimental data is generally satisfactory indicating that the pdf equation model and the moment method can quantitatively describe the statistics of free turbulence. Additionally, the balance of turbulence energy was calculated and discussed subsequently. It shows that the pdf methods are of more potential in revealing turbulence structure than conventional turbulence models.