On Oberbeck's vortices

Abstract

The detailed structure of the liquid-vortices produced by Oberbeck's experiments has been studied in this paper. An automatic arrangements was introduced into the apparatus, so that the same vortex could be reproduced any number of times. The stream-lines in the moving liquid were traced by colouring its specific parts, and these were photographed at various stages of the motion. The space-time relationship was obtained by cinematographic films with an arrangement for recording time. A longitudinal section of the moving liquid shows that the stream-lines have the form of a double-spiral advancing through time liquid and at the same time presenting an increased number of convolutions, and followed by a "tail." The "tail" contracts, and after a time the spirals close up, and the moving liquid is transformed to an anchor-shaped vortex and is tiredly dissipated away. It appears that there are three distinct stages in the life-history ot the vortex. In the first stage it is under the influence of the tube, in the second stage it is freely developing uninfluenced by the boundary, and in the third stage it transforms itself into an anchor-shaped vortex and meets with dissolution. Each of these stages is associated with a distinct change in the structure and the rotational motion of the vortex. These have been studied in detail in this paper. A mathematical theory has been given which explains the essential features of the motion.