Nonlinear modes in the hollow-cores of liquid vortices

Abstract

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. © 2013 Elsevier Masson SAS. All rights reserved.