Characteristics of Reynolds Shear Stress in Adverse Pressure Gradient Turbulent Boundary Layers

Abstract

The focus of the present work is to characterize the features of the turbulent inertia term (the wall-normal gradient of Reynolds shear stress) through the mean momentum balance and the Reynolds shear stress correlation coefficient ($\rho _{uv}$). Effects of the Reynolds number and Clauser pressure-gradient parameter, $\beta$, are discussed. Large eddy simulations of low Reynolds number adverse pressure gradient turbulent boundary layers from Bobke et al. [1], low Reynolds number experimental data from Vila et al. [2] and Volino [3], and newly acquired experimental data at higher Reynolds number from the Flow Physics Facility at The University of New Hampshire are utilized for this analysis. Observations are compared to zero pressure gradient turbulent boundary layer direct numerical simulations of Schlatter and Örlu [4] and Sillero et al. [5], and experimental data from Zimmerman et al. [6] and Zimmerman [7]. These cases show that the correlation coefficient ($\rho _{uv}$) decreases in magnitude with increasing Reynolds number and $\beta$. However, from these initial observations we find that $\rho _{uv}$ is more sensitive to changes in the Reynolds number in comparison to the examined range of $\beta$. We also find that the location of zero-crossing of the turbulent inertia term seems to scale with $\sqrt{\delta ^+}$ while the minimum of $\rho _{uv}$ scales with $\delta$.