A technique used in these kinds of situations is EMS, or Electromagnetic Stirring. The idea is to induce motion in a fluid, just by applying an electric field and a magnetic field in perpendicular directions. Another research area where these fields come together is controlling turbulence in a fluid flow, using electromagnetic forces. Furthermore, electrodynamically driven fluid flows have astrophysical and geophysical relevance as well.
The physical setup I focused on for the summer research project is essentially a thin annular layer of electrolytic fluid, driven by electromagnetic forces. When we add some dye to watch the flow – what do we see? a number of vortex patterns – close to the outer edge of the fluid layer. I would encourage taking a look at the picture from the report to actually see for yourself what these patterns are. These vortices grow, interact with each other, and eventually die out. What significance does this observation have? The evolution of these vortices could be used to describe how well the fluid has mixed itself. This is why we attempt to algebraically establish how the amplitudes of these modes evolve over time.
We began by assuming the simplest possible relationship for the amplitude evolution and smallest possible amount of vortical modes, and then added terms and modes until a meaningful solution is obtained. After the system of amplitude evolution equations was obtained, we analysed the phase portraits of the resulting dynamical system, alongside a numerical solution to the same system. Hence, we were able to algebraically and graphically establish the evolution of the amplitude equations considering 1 periodic and 1 aperiodic mode. Further scope would be to add extra modes to the system so that it better replicates the actual number of vortical modes observed.
Swinburne University of Technology