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Polygonal instabilities on interfacial vorticities.

M Labousse1,2, J W M Bush3

  • 1Institut 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.

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Summary
This summary is machine-generated.

This study reveals two instability mechanisms, surface tension and fluid inertia, that can destabilize toroidal vortices, causing them to change shape. These findings are relevant to understanding fluid dynamics in various experimental setups.

Keywords:
Flowing Matter: Interfacial phenomena

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Area of Science:

  • Fluid dynamics
  • Theoretical physics
  • Interface phenomena

Background:

  • Toroidal vortices are complex fluid structures with applications in various scientific fields.
  • Understanding the stability of these vortices is crucial for predicting their behavior and controlling fluid flow.
  • Previous research has explored vortex dynamics, but the specific instabilities of interface-bound toroidal vortices require further investigation.

Purpose of the Study:

  • To theoretically investigate the stability of a toroidal vortex confined by an interface.
  • To identify the primary mechanisms responsible for the instability and shape transformation of these vortices.
  • To provide a theoretical framework for interpreting experimental observations of toroidal vortex behavior.

Main Methods:

  • Utilizing theoretical analysis to model the behavior of interface-bound toroidal vortices.
  • Identifying and characterizing instability mechanisms driven by surface tension effects.
  • Identifying and characterizing instability mechanisms driven by fluid inertia.

Main Results:

  • Two distinct instability mechanisms were identified: one driven by surface tension and another by fluid inertia.
  • Either of these mechanisms can lead to the transformation of a circular torus into a polygonal shape.
  • The theoretical predictions offer explanations for phenomena observed in related experiments.

Conclusions:

  • The stability of interface-bound toroidal vortices is governed by a interplay between surface tension and fluid inertia.
  • These instabilities can lead to significant shape changes, transitioning from circular to polygonal forms.
  • The findings provide valuable insights for experimental studies involving toroidal vortex rings, hydraulic jumps, and hydraulic bumps.