Eur. Phys. J. E (2015) 38: 113
https://doi.org/10.1140/epje/i2015-15113-5

Regular Article

Polygonal instabilities on interfacial vorticities

¹ Institut Langevin, ESPCI Paristech, CNRS - UMR 7587, PSL Research University, Université Pierre and Marie Curie, 1 rue Jussieu, 75005, Paris, France
² Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Sorbonne Paris Cité, CNRS - UMR 7057, 10 Rue A. Domon and L. Duquet, 75013, Paris, France
³ Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139, MA, Cambridge, USA

^* e-mail: matthieu.labousse@univ-paris-diderot.fr
^** e-mail: bush@math.mit.edu

Received: 19 May 2015
Revised: 21 September 2015
Accepted: 28 September 2015
Published online: 30 October 2015

Abstract

We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.