### Abstract

A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is 'persistent'. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations. (Authors)

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

Pages (from-to) | 415-444 |

Number of pages | 30 |

Journal | Journal of Fluid Mechanics |

Volume | 236 |

State | Published - 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*236*, 415-444.

**The kinematics of stretching and alignment of material eleme.** / Dresselhaus, E.; Tabor, Michael.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 236, pp. 415-444.

}

TY - JOUR

T1 - The kinematics of stretching and alignment of material eleme

AU - Dresselhaus, E.

AU - Tabor, Michael

PY - 1992

Y1 - 1992

N2 - A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is 'persistent'. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations. (Authors)

AB - A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is 'persistent'. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations. (Authors)

UR - http://www.scopus.com/inward/record.url?scp=0026792094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026792094&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026792094

VL - 236

SP - 415

EP - 444

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -