### Abstract

Folding of material filaments was examined computationally in the three-dimensional flow in a cylindrical duct with helical deflectors by tracking the curvature of line elements in the flow. Two geometries were analyzed: a configuration in which the flow is globally chaotic, and an alternative geometry which has a mixture of chaotic and regular motion. The behavior of the curvature field in this complex flow geometry was in agreement with that previously observed for much simpler two-dimensional model flows [Phys. Fluids 8, 75 (1996)]. Curvature profiles along individual element trajectories indicate that an inverse relationship exists between the rates of stretching and curvature. Material elements are compressed when they are folded. After an initial transient, the mean curvature oscillates within a finite range with a periodicity matching that of the flow geometry. The spatial structure of the curvature field becomes period-independent, and the probability density functions of curvature computed for different numbers of periods collapse to an invariant, self-similar distribution without the need for scaling.

Original language | English (US) |
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Pages (from-to) | 1942-1952 |

Number of pages | 11 |

Journal | Physics of Fluids |

Volume | 10 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1998 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*10*(8), 1942-1952. https://doi.org/10.1063/1.869710

}

*Physics of Fluids*, vol. 10, no. 8, pp. 1942-1952. https://doi.org/10.1063/1.869710

**The curvature of material lines in a three-dimensional chaotic flow.** / Hobbs, D. M.; Muzzio, Fernando.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The curvature of material lines in a three-dimensional chaotic flow

AU - Hobbs, D. M.

AU - Muzzio, Fernando

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Folding of material filaments was examined computationally in the three-dimensional flow in a cylindrical duct with helical deflectors by tracking the curvature of line elements in the flow. Two geometries were analyzed: a configuration in which the flow is globally chaotic, and an alternative geometry which has a mixture of chaotic and regular motion. The behavior of the curvature field in this complex flow geometry was in agreement with that previously observed for much simpler two-dimensional model flows [Phys. Fluids 8, 75 (1996)]. Curvature profiles along individual element trajectories indicate that an inverse relationship exists between the rates of stretching and curvature. Material elements are compressed when they are folded. After an initial transient, the mean curvature oscillates within a finite range with a periodicity matching that of the flow geometry. The spatial structure of the curvature field becomes period-independent, and the probability density functions of curvature computed for different numbers of periods collapse to an invariant, self-similar distribution without the need for scaling.

AB - Folding of material filaments was examined computationally in the three-dimensional flow in a cylindrical duct with helical deflectors by tracking the curvature of line elements in the flow. Two geometries were analyzed: a configuration in which the flow is globally chaotic, and an alternative geometry which has a mixture of chaotic and regular motion. The behavior of the curvature field in this complex flow geometry was in agreement with that previously observed for much simpler two-dimensional model flows [Phys. Fluids 8, 75 (1996)]. Curvature profiles along individual element trajectories indicate that an inverse relationship exists between the rates of stretching and curvature. Material elements are compressed when they are folded. After an initial transient, the mean curvature oscillates within a finite range with a periodicity matching that of the flow geometry. The spatial structure of the curvature field becomes period-independent, and the probability density functions of curvature computed for different numbers of periods collapse to an invariant, self-similar distribution without the need for scaling.

UR - http://www.scopus.com/inward/record.url?scp=0032133537&partnerID=8YFLogxK

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U2 - 10.1063/1.869710

DO - 10.1063/1.869710

M3 - Article

AN - SCOPUS:0032133537

VL - 10

SP - 1942

EP - 1952

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 8

ER -