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

D. M. Hobbs, Fernando Muzzio

Research output: Contribution to journalArticle

16 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1942-1952
Number of pages11
JournalPhysics of Fluids
Volume10
Issue number8
DOIs
StatePublished - Jan 1 1998

Fingerprint

curvature
flow geometry
three dimensional flow
deflectors
geometry
two dimensional models
probability density functions
ducts
folding
fluid flow
periodic variations
filaments
trajectories
scaling
profiles
configurations

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

@article{c3a088792e5849f4a6f33630bfce0de7,
title = "The curvature of material lines in a three-dimensional chaotic flow",
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.",
author = "Hobbs, {D. M.} and Fernando Muzzio",
year = "1998",
month = "1",
day = "1",
doi = "10.1063/1.869710",
language = "English (US)",
volume = "10",
pages = "1942--1952",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics Publising LLC",
number = "8",

}

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

In: Physics of Fluids, Vol. 10, No. 8, 01.01.1998, p. 1942-1952.

Research output: Contribution to journalArticle

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

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

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 -