Boundary-layer waves and transition

Abstract

On the basis of observations with hydrogen bubble photographs the following picture for the origin of the strong instability behind the splitting point of Tollmien waves has been proposed: beyond a certain threshold, characterized by a combination of wave amplitude and Reynolds number and inside the Tollmien wave at a phase position near the center of the cat's-eye there emerges a weak local vorticity peak. This peak does not move relative to the surrounding matter and therefore resembles an ordinary vortex tube. Beyond the threshold it will develop its own warping instability which splits the amplification rate of the Tollmien waves. The three dimensional bending or warping of vortex tubes inside a boundary layer leads to different transport velocities or a convection which stretches the vortex tubes. The stretch in turn produces more convection and so, within the range of one or two wave lengths of the Tollmien waves the vorticity distribution is not only converted into an oblique orientation, but also concentrated into a top- and tail-vortex. The first one will be observed by a hot wire probe as a single spike. It is therefore concluded that the whole development between the splitting point and the appearance of a single spike is a continuous and coherent physical phenomenon.