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.