Correlations among turbulent shear stress, turbulent kinetic energy, and axial turbulence intensity

The validity of the formula that states a linear relationship between the mean value of UV divided by shear velocity squared and the nondimensional turbulent kinetic energy of the flow was examined in relation to (1) the inlet region of pipe and channel flows, (2) the inner layer of duct flow, and (3) the effect of surface roughness. Data from the literature were analyzed. It is found that the linear relationship is, in general, not accurate when applied to pipe and channel flows. In such flows, however, the turbulent kinetic energy varies linearly with the axial component of turbulence intensity. Linearity holds for rough and smooth ducts, for the inner and outer layers, and over a range of Reynolds numbers. The parameters for these valid linear relationships were determined.