On the flow of air behind an inclined flat plate of infinite span

Abstract

The general form of the flow behind an infinitely long thin flat plate inclined at a large angle to a fluid stream of infinite extent has been known for many years past. The essential features of the motion are illustrated in the smoke photograph given in fig. 1, Plate 6. At the edges, thin bands of vorticity are generated, which separate the freely-moving fluid from the “dead-water” region at the back of the plate; and at some distance behind, these vortex bands on account of their lack of stability roll up and form what is now commonly known as a vortex street (see fig. 2). Various theories for calculating the resistance of the plate have also been advanced from time to time. One of the earliest is the theory of “discontinuous” motion due to Kirchhoff and Rayleigh, who obtained the expression π sin α/4 + π sin α ρV 0 2 b (see symbols) for the normal force per unit length of the plate. More recently Kármán has obtained a formula for the resistance of a plate normal to the general flow, in terms of the dimensions of the vortex system at some distance behind the plate. In spite, however, of these and other important investigations, much more remains to be discovered before it can be said that the phenomenon of the flow is completely understood. No attempt has hitherto been made, as far as the writers are aware, to determine experimentally, at incidences below 90°, the frequency and speed with which the vortices pass downstream; the dimensions of the vortex system; the average strength of the individual vortices; or the rate at which vorticity is leaving the edges of the plate. The present investigation has been undertaken to furnish information on these features of the flow.