An Attempt to Use Mechanical Energy Conservation Principle in Case of Channel Developed Turbulent Flow

Abstract

In this work a hypothesis about the fluid flow character is proposed which consists in the splitting of a flow in two parts. The first one is treated dynamically, and the second statistically. The instability generating energy coming from the dynamical flow being distributed by the statistical flow results in an influence on the first one and forms the observed flow. The connection between the two flows is obtained by the requirement of the mechanical energy conservation. A corresponding model is analyzed in some details and applied to the case of developed turbulence in a channel Poiseuille flow. The mean velocity profiles for values of $Re =$ 13800, 23200, 32800 are computed and compared with the existing experimental data. Numerically derived velocity profiles with $Re$ from 100 to 143000 are given.