The initial roll-up of a thick, two-dimensional wake behind a wing of finite span

Abstract

Many investigators have studied the rolling-up of the vortex wake behind a wing of finite span. The earliest step in this study was the work of Kaden who found an analytical solution for the rolling-up with time of a semi-infinite, straight, two-dimensional vortex sheet. This solution must represent the situation very close to the edges of a finite-span vortex sheet of zero thickness, in two or three dimensions, during the initial stage of the rolling-up process. An important result following from Kaden’s work is that, from the very onset of rolling-up, due to the infinite velocity at the sheet edge, a spiral of near-axi-symmetric form, with an infinite number of turns, is established at the edge. This is a consequence of the assumption of zero thickness for the sheet.