Soft Matter and Complex Systems Seminar

The Taylor-Couette system-the flow between two concentric rotating cylinders, has served as a model problem for studying flow instabilities and transitions to turbulence. In the first part of this seminar, I will briefly trace its historical importance and discuss how simple variations in rotation rates and geometry give rise to a hierarchy of flow states, from steady Taylor vortices to complex wavy and turbulent regimes. Extending the problem to non-circular enclosures introduces additional confinement effects and even Moffatt-like vortices, enriching the dynamics further.
In the second part, I will outline how meshless numerical methods can be employed to simulate such flows efficiently without requiring structured grids. Finally, I will present results from simulations, some using these meshless methods, that exhibit vortex patterns, including one reminiscent of the hexagonal jet observed in Saturn’s atmosphere. While not being an exact planetary model, the similarity highlights the universality of pattern-forming mechanisms in rotating shear-driven flows.