Layered structure of turbulent plane wall jet

Based on the force balances in the mean momentum equation, a turbulent plane wall jet is divided into three regions: a boundary-layer-like region (BLR) adjacent to the wall, a half-free-jet-like region (HJR) away from the wall, and a plug-flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity $U_\mathrm{max}$, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall $|V_\infty|$ and a proper scale for the Reynolds shear stress is $U_\mathrm{max}|V_\infty|$, similar to those in a turbulent free jet. The BLR region can be further divided into four sub-layers, similar to those in a canonical pressure- or shear-driven wall-bounded turbulent flow. Building on the log law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.