Experimental demonstration of the water-holding property of three-dimensional vortices. (17th September 2018) - Tél, T.
Abstract: When injecting dye into a vertical vortex generated by a commercial magnetic stirrer, one finds that dye remains captured around the vortex core over minutes, while it gets mixed with the water outside this region rather rapidly. Thus, considering its horizontal motion, the dye becomes trapped within a critical radius, even though the vortex structure (and the dyed region) is aperiodically time-dependent due to the oscillations of the position of the stirring bar. According to a recent paper by Haller and coworkers ( J. Fluid Mech., 795 (2016) 136), three-dimensional time-dependent vortices should be defined as rotating, material-holding tubular regions of the fluid. We report here about a set of experiments carried out with magnetic-stirrer-generated vortices which appears to provide the first pieces of evidence supporting the theory in a very elementary set-up that is accessible even in high schools. Our data also provide information about quantities not predicted by the theory, e.g., the lifetime of dye spent within the vortex. We show that the maximum radius of the stable dye cylinders, i.e., the horizontal extent of the vortex, hardly depends on the rotational frequency of the stirrer bar –at least in the range investigated –but increases with the length of the bar. A generalization of this finding leads to the conclusion that the size of the material-holding region of the vortices in nature should be proportional to the size of the surface (or pressure) depression accompanying the vortex.