We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application of dynamical systems theory tools. As an illustration of the utility of the symmetry reduction, we apply it to a model of the pilot-wave system with a central harmonic force. We begin our analysis by identifying local bifurcations and the onset of chaos. We then describe the emergence of chaotic regions and their merging bifurcations, which lead to the formation of a global attractor. In this final regime, the droplet’s angular momentum spontaneously changes its sign as observed in the experiments of Perrard et al. [Phys. Rev. Lett. 113(10), 104101 (2014)].
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January 2019
Research Article|
January 22 2019
State space geometry of the chaotic pilot-wave hydrodynamics
Nazmi Burak Budanur;
Nazmi Burak Budanur
a)
1
Nonlinear Dynamics and Turbulence Group, IST Austria
, 3400 Klosterneuburg, Austria
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Marc Fleury
Marc Fleury
2
Freeside LLC
, 3344 Peachtree Rd., Atlanta, Georgia 30326, USA
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a)
Electronic mail: burak.budanur@ist.ac.at
Chaos 29, 013122 (2019)
Article history
Received:
September 18 2018
Accepted:
December 18 2018
Connected Content
A correction has been published:
Publisher’s Note: “State space geometry of the chaotic pilot-wave hydrodynamics” [Chaos 29, 013122 (2019)]
Citation
Nazmi Burak Budanur, Marc Fleury; State space geometry of the chaotic pilot-wave hydrodynamics. Chaos 1 January 2019; 29 (1): 013122. https://doi.org/10.1063/1.5058279
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