### Abstract

This paper deals with a comparison between experimental observations in low-Reynolds-number wake behind an oscillating cylinder and the universal properties of sine circle map. When the limit cycle due to the natural vortex shedding in the wake is modulated at a second frequency by oscillating the cylinder transversely, one obtain in phase space a flow on a two torus. The nonlinear interaction between the two oscillators in Arnol's tongues due to phase locking, the devil's staircase along the critical line, and a transition from order to chaos via the quasiperiodic route. The sine circle map describes these features adequately. A comparison between the experiment and the theory is made in terms of multifractal formalism and trajectory scaling function.

Original language | English (US) |
---|---|

Pages (from-to) | 693-703 |

Number of pages | 11 |

Journal | Pramana - Journal of Physics |

Volume | 48 |

Issue number | 2 |

State | Published - Feb 1997 |

### Fingerprint

### Keywords

- Chaos
- Circle maps
- Universality
- Wakes

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Pramana - Journal of Physics*,

*48*(2), 693-703.

**The onset of chaos in the wake of an oscillating cylinder : Experiment and the dynamics of the circle map.** / Olinger, D. J.; Chhabra, A. B.; Sreenivasan, K. R.

Research output: Contribution to journal › Article

*Pramana - Journal of Physics*, vol. 48, no. 2, pp. 693-703.

}

TY - JOUR

T1 - The onset of chaos in the wake of an oscillating cylinder

T2 - Experiment and the dynamics of the circle map

AU - Olinger, D. J.

AU - Chhabra, A. B.

AU - Sreenivasan, K. R.

PY - 1997/2

Y1 - 1997/2

N2 - This paper deals with a comparison between experimental observations in low-Reynolds-number wake behind an oscillating cylinder and the universal properties of sine circle map. When the limit cycle due to the natural vortex shedding in the wake is modulated at a second frequency by oscillating the cylinder transversely, one obtain in phase space a flow on a two torus. The nonlinear interaction between the two oscillators in Arnol's tongues due to phase locking, the devil's staircase along the critical line, and a transition from order to chaos via the quasiperiodic route. The sine circle map describes these features adequately. A comparison between the experiment and the theory is made in terms of multifractal formalism and trajectory scaling function.

AB - This paper deals with a comparison between experimental observations in low-Reynolds-number wake behind an oscillating cylinder and the universal properties of sine circle map. When the limit cycle due to the natural vortex shedding in the wake is modulated at a second frequency by oscillating the cylinder transversely, one obtain in phase space a flow on a two torus. The nonlinear interaction between the two oscillators in Arnol's tongues due to phase locking, the devil's staircase along the critical line, and a transition from order to chaos via the quasiperiodic route. The sine circle map describes these features adequately. A comparison between the experiment and the theory is made in terms of multifractal formalism and trajectory scaling function.

KW - Chaos

KW - Circle maps

KW - Universality

KW - Wakes

UR - http://www.scopus.com/inward/record.url?scp=0031072238&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031072238&partnerID=8YFLogxK

M3 - Article

VL - 48

SP - 693

EP - 703

JO - Pramana - Journal of Physics

JF - Pramana - Journal of Physics

SN - 0304-4289

IS - 2

ER -