Related Experiment Video
Updated: Aug 19, 2026

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
Published on: May 9, 2021
Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics
Jan Abshagen1, Juan M Lopez, Francisco Marques
1Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany.
Abstract:
The combined experimental and numerical study finds a complex mechanism of Z(2) symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the Z(2) symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z(2)-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of Z(2) symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.
Related Concept Videos
Symmetry in Maxwell's Equations
Bessel Function of Order Zero
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.
Deformations in a Symmetric Member in Bending
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Unsymmetric Bending
Gauss's Law: Cylindrical Symmetry

