On the flow near the trailing edge of a flat plate

Abstract

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l, generally valid near the plate when the Reynolds number Re is large, fails within a distance O(lRe^-3/4) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O(Re^-3/4) and the multiplicative constant is explicitly worked out for the linearized equations.