title: Polygonal instabilities on interfacial vorticities.
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.
authors.affiliation: Institut Langevin, ESPCI Paristech, CNRS - UMR 7587, PSL Research University, Université Pierre and Marie Curie, 1 rue Jussieu, 75005, Paris, France. matthieu.labousse@univ-paris-diderot.fr.|Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Sorbonne Paris Cité, CNRS - UMR 7057, 10 Rue A. Domon and L. Duquet, 75013, Paris, France. matthieu.labousse@univ-paris-diderot.fr.
authors.forename: M
authors.initials: M
authors.lastname: Labousse
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139, MA, Cambridge, USA. bush@math.mit.edu.
authors.forename: J W M
authors.initials: JW
authors.lastname: Bush
keywords: Flowing Matter: Interfacial phenomena