Nonlinear modes in the hollow-cores of liquid vortices

•We model the polygonal wave pattern observed within hollow-core vortex.•The model is nonlinear; it predicts fairly well the experimental observations.•The model is the first attempt to model polygonal patterns of this kind.•By analogy, the model can be relevant to confined electron columns.

In this paper we show that the wave patterns observed on the interfacial contours of hollow-core vortices, produced within a shallow layer of fluid contained in stationary cylinder and driven by a rotating disk at the bottom [G.H. Vatistas, H.A. Abderrahmane, M.H. Kamran Siddiqui, Experimental confirmation of Kelvin’s equilibria, Phys. Rev. Lett. 100 (2008) 174503–174504], can be described as travelling cnoidal waves. These rotating stationary waves are obtained as solutions of a Korteweg–de Vries type equation, in accordance with the geometrical and kinematic characteristics of the observed polygonal patterns.