Letter: New boundary layer structures due to strong wall slippage

In a laminar boundary layer flow, the extent of slip is not fixed but varies with the slip length λ relative to the boundary layer thickness δ. Here, we report that distinct boundary layer structures can arise from slip effects when λ exceeds δ. This is demonstrated by revisiting two closely related problems in the presence of wall slip: (i) the Stokes 1st problem and (ii) a steady high Reynolds number boundary layer flow driven by a moving plate (of length L). In (i), the wall stress is found to be constant for δ ≪ λ for short times and persists until time t reaches the slip-stick transition (SST) point t_λ ∼ λ²/ν (with ν being the kinematic viscosity) after which the usual no-slip result t^−1/2 takes over. A similar transition can also occur spatially to (ii). We show that the boundary layer can turn from the thicker one δ ∼ LRe^−1/2 ≫ λ in the weak-slip regime to the thinner one δ ∼ L(λ/L)^1/3 Re^−1/3 ≪ λ in the strong-slip regime. This boundary layer structure change is also accompanied by a shift from the well-known no-slip friction law C_f ∼ Re^−1/2 to the strong-slip law C_f ∼ (L/λ)Re⁻¹ when increasing the Reynolds number Re = UL/ν beyond the SST point Re_c ∼ (L/λ)². Generalization to the Falkner-Skan wedge flow is also made, suggesting that similar friction law and boundary layer structure changes might occur in a wide class of wall-bounded boundary layer flows.