Shape factor of the turbulent boundary layer on a flat plate and the Reynolds shear stress in the outer region

It has recently been shown by Wei and Klewicki [Phys. Rev. Fluids 1, 082401 (2016)] that in a zero-pressure-gradient turbulent boundary layer flow, the product of the nondimensional free-stream velocities in the streamwise $\left(U_{\infty }^{+}\right)$ and wall-normal $\left(V_{\infty }^{+}\right)$ directions is the flow shape parameter $\left(H\right)$: $U_{\infty }^{+}{V}_{\infty }^{+}=H$. It is suggested here that this result is a consequence of the variation of the Reynolds shear stress with $U_{\infty }V$ in the outer region of the boundary layer.

Figure 1

(a–c) Variation of $U_{\infty }^{+}{V}^{+}$ with the Reynolds shear stress. (d–f) Comparison of $C^{+}$ (open symbol) with the shape parameter (filled symbol). Data shown are Schlatter and Örlü [6] in panels (a) and (d), Simens et al. [5] in panels (b) and (e), and Eitel-Amor et al. [7] in panels (c) and (f).