My research develops a theoretical model to predict the properties of symmetry-breaking polygons formed on a rotating fluid surface.
When a circular plate is rotated at the bottom of a cylindrical vessel containing fluid, the fluid surface can form stable polygons under certain conditions. This phenomenon is very surprising, as it seems that the rotational symmetry of the setup is mysteriously broken when polygons are formed. I experimentally measured the geometries of the formed polygons and studied their dependence on parameters such as the plate rotational rate. Both the number of sides and the sizes of the polygons were found to increase when the plate rotated faster.
In my research, I sought to develop a theoretical model that could accurately predict the properties of the formed polygons in agreement with experimental results. Taking on a novel approach of analysing the forces on a fluid particle travelling along the boundary of the polygon, the mechanism of polygon formation and the effect of the plate rotation on the polygons were physically understood. Applying it quantitatively, with considerations on the properties of the fluid flow, a differential equation governing the polygon’s steady-state geometry was formulated. A high degree of predictive power into the shape of the polygon was achieved, closely matching experimental data.