Rotating Polygon Instability on the free surface of rotating liquid nitrogen in Leidenfrost state

When liquid nitrogen is poured into a warm pot, film boiling will create a Leidenfrost effect insulating the liquid from the pot by a thin air-layer strongly reducing the friction. Stirring the fluid layer in a cylindrical pot will thus create a long-lived vortex whose free surface can deform into polygons as described in Toph{\o}j \textit{et al}., Phys. Rev. Lett. \textbf{110}, 194502 (2013). We have investigated the relation of these instabilities to the stationary rotating polygons described in Vatistas, J. Fluid Mech. \textbf{217}, 241 (1990) and Jansson \textit{et al.}, Phys. Rev. Lett. \textbf{96}, 174502 (2006) as well as to the theory by Toph{\o}j et al. We further discuss the possible relation to the hexagonal north polar vortex of Saturn (D. A. Godfrey, Icarus, \textbf{76}. 335 (1988)). Compared to earlier experiments, the nitrogen flows appear strongly turbulent with violent bursts generating droplets. It is remarkable that they can still maintain well-defined polygonal structures that appear to be rotating like a solid body. We quantify the shape changes by the spectral dynamics of the contact line in the bottom of the pot.