Skin friction in zero-pressure-gradient boundary layers

A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_δ\rightarrow \infty$, the dynamically defined boundary layer thickness $δ(x)\propto x/\ln^{2}Re_{x}$ and the skin friction $λ=\frac{2τ_{w}}{ρU_{0}^{2}}\propto 1/\ln^{2}δ(x)$. Here $τ_{w}$ and $U_{0}$ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter $\frac{dδ(x)}{dx}\rightarrow 0$ in the limit $x\rightarrow \infty$.

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