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The similarity between turbulent heat transfer and Reynolds stress is investigated using the equations written in Lagrange description. The correlation between pressure gradient fluctuation in the flow direction and wall-normal velocity [term (B)] depresses the Reynolds stress, which makes the turbulent Prandtl number Prt less than unity. Based on the trajectories of fluid particles, an algebraic equation was theoretically derived to correlate the term (B) to Prt. Using the database of the trajectories calculated by DNS, the change of Prt with regard to (B) was actually estimated from the equation. The slight decrease of (B) causes the dramatic reduction of Prt in the log-law region, while the change of Prt in the near-wall region is hardly recognized. This is caused by the fact that the Reynolds stress or turbulent heat transfer in the log-law region are influenced by the fluid particles coming from further positions compared with the near-wall region.

The Influence of Pressure Gradient-Wall Normal Velocity Correlation on Turbulent Prandtl Number