Structure of Steady Closed Streamline Flows within a Boundary Layer

Abstract

Numerical solutions to the full Navier‐Stokes equations have been obtained for flow past a flat plate of length L in which a finite slip velocity U 0 opposite in direction to that of the free stream is imposed. These solutions, which covered the range 0 ≤|U 0 /U ∞ | ≤ 0.4 and 0.1 ≤ Re ≤ 80 with U ∞ being the freestream velocity and Re the Reynolds number U ∞ L/ν , strongly suggest that, as Re → ∞, the region of closed streamline flow adjacent to the plate decreases in width as Re −1/2 and thus remains imbedded within the viscous layer for all Re. In turn, this implies that, as Re → ∞ , the flow field near the plate, including even the recirculating region, is described by the parabolic boundary‐layer equations.