Dynamics of spinning discs in fluids
Creators: name: Gorce, Jean-Baptiste
Publisher: name: The Australian National University
Year: 2021

description: The dynamics associated with spinning bodies are important in numerous processes in both nature and industry. A spinning body in a fluid produces a vortex and transfers angular momentum to the surrounding fluid via a combination of viscous dissipation and inertial effects. When a spinning body is moving through a fluid, the interaction between the vortex and the flow affects its trajectory. This motion is complex due to the instabilities developing in the flow field. This thesis aims to investigate the dynamics of spinning discs on the water surface. The focus of the study are the vortex structure generated by a spinning disc, and the forces acting on the discs on the surface of a liquid at rest and in a nonuniform flow. During the thesis, we report on the self-guided propulsion of magnetic fast-spinning disc on a liquid surface in the presence of a solid boundary. Above a critical spinning frequency (higher rotational Reynolds numbers), such discs generate localized 3D vortices and form composite "spinner-vortex" quasiparticles with nontrivial, yet robust dynamics. It is found that an isolated spinning disc in an unbounded fluid performs chaotic motions while its motion becomes deterministic as the disc approaches a solid boundary. Such spinner-vortices are attracted and dynamically trapped near the boundaries, propagating along the wall of any shape similarly to "liquid wheels." The propulsion velocity and the distance to the wall are controlled by the angular velocity of the disc via the balance between the Magnus and wall repulsion forces. Rotating particles at the liquid-gas interface can be efficiently manipulated using the surface-wave analogous to optical lattices. Two orthogonal standing waves generate surface flows of counter-rotating half-wavelength unit cells, the vortex lattice or liquid-metamaterials, whose geometry is controlled by the wave phase shift. We discuss forces acting on a spinning disc carried by a nonuniform flow and show how the forces confine the spinning disc to orbit inside the same-sign vortex cells of the wave-driven flow. Reversing the spin, we move the disc into an adjacent cell. By changing the spinning frequency or the wave amplitude, one can precisely control the disc orbit. Multiple discs within a unit cell self-organize into stable patterns, e.g., triangles or squares, orbiting around the centre of the cell. Spinning discs having different frequencies can also be confined, such that the higher-frequency spinner occupies the inner orbit and the lower-frequency one circles on the outer orbit, while the orbital motions of both discs are synchronized. The results provide a better understanding of the dynamics of spinning bodies in fluids and illustrate the importance of the interaction between the vortex generated by the spinning body and the surrounding flow in applications such as turbine flow or the motion of spinning projectiles. Our results offer a new type of surface vehicle and provide a powerful tool to manipulate spinning objects in fluids. By placing active magnetic discs inside a liquid vortex, a powerful tool is created, that allows manipulation and self-assembly of spinning discs, turning them into vehicles capable of transporting matter and information between autonomous unit cells.