A new turbulence analysis method based on the mean speed and mean free path theory of the molecule thermal motion—correction and Improvement

Based on the mean speed and mean free path theory of the molecule thermal motion, a mathematical formulation of the Reynolds stress by reasonable analysis and derivation has been obtained and the result have been published in the Journal of Physics A. In follow-up studies, certain flaws were detected in the mathematical derivation presented in my previous paper and therefore the final mathematical expressions of the Reynolds shear stress achieved are not very accurate. In this paper, these flaws have been fixed and a new form of mathematical expression of Reynolds shear stress has been proposed. In addition, the mathematical expression of the Reynolds normal stress was also derived. •A mathematical formulation of the Reynolds stress is obtained from this study.•Reynolds shear stress is proportional to the mean free path and temperature.•Reynolds shear stress is inversely proportional to the square of pressure.•Reynolds shear stress is inversely proportional to the effective molecular diameter.•The nature of turbulence is chaos in flow field caused by molecular thermal motion.