Standing Vortex-Pair behind a Flat Plate Normal to Uniform Flow of Viscous Fluid

Abstract

The critical Reynolds number is discussed at which a standing vortex-pair first appears behind a flat plate set normal to steady viscous uniform flow. The size of the vortex-pair at small Reynolds numbers is evaluated by making use of the 7th approximate solution of the Oseen equation and the result is compared with existing experimental data. It is also shown that the vorticity is zero everywhere on the plate to the lowest order of the Reynolds number expansion. A next order local solution of the Navier-Stokes equation is considered in the vicinity of the edge of the plate. From these analysis, it is concluded that the critical Reynolds number in question is zero and the flow separates at the edges of the plate at any small but finite Reynolds number.