New boundary layer structures due to wall slippage

We demonstrate that wall slip can significantly modify temporal and spatial structures of boundary layer flows. Two benchmark problems for flow generated by a moving plate are re-investigated to reveal how the boundary layer thickness $\delta $ and the slip length $\lambda $ determine flow characteristics: (i) Stokes's first problem, and (ii) Blasius's problem. In (i), the solution is found to combine the features of two problems: (a) simple vorticity diffusion driven by a constant wall stress created by strong wall slippage, and (b) the classical Stokes first problem driven by a no-slip moving plate, characterizing short time and long time solution behaviors, respectively. A similar slip-to-no-slip transition can occur \textit{spatially} to (ii), leading the friction law to change from the well-known Blasius law $C_{\mathrm{f}} \sim $ \textit{Re}$^{-1/2}$ to the free-surface-like result $C_{\mathrm{f}} \sim $ ($L$/$\lambda )$\textit{Re}$^{-1}$ when the Reynolds number \textit{Re} (based on the plate length $L)$ is greater than ($L$/$\lambda )^{2}$.