Abstract
Based on the mean speed and mean free path theory of the molecule thermal motion, we obtain a mathematical formulation of the Reynolds stress by reasonable analysis and derivation. Results show that in the case of non rarefied gas flow, the Reynolds stress is inversely proportional to three parameters: the number of molecule in unit volume, the square root of the molecule mass and the square of the effective diameter of the molecule. Meanwhile, the Reynolds stress is proportional to other two parameters: the square of the temperature; the gradient of time-averaged velocity in the flow field. The essence of turbulence is the chaos resulted from the molecule thermal motion in non uniform flow field.
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