### 抄録

A new linear instability mechanism of curvature origin is established for a vortex ring. The curvature effect reduces O(2) × SO(2) symmetry of a circularcylindrical tube to O(2), and fuels a pair of Kelvin waves whose azimuthal wavenumbers on the core are separated by one. For Kelvin's vortex ring, the growth rate and eigenfunctions are written out in closed form. In the inviscid case, the curvature effect dominates over the elliptically straining effect, but the former suffers from enhanced viscous damping. There are numerous excitable modes. As a first step toward an understanding of the route to a matured stage, we derive equations for weakly nonlinear evolution of amplitudes of the curvature instability. Our direct numerical simulation successfully captures the elliptical instability.

元の言語 | 英語 |
---|---|

ホスト出版物のタイトル | IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamicsa |

ページ | 283-294 |

ページ数 | 12 |

巻 | 79 |

出版物ステータス | 出版済み - 2006 |

### 出版物シリーズ

名前 | Fluid Mechanics and its Applications |
---|---|

巻 | 79 |

ISSN（印刷物） | 09265112 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering
- Mechanics of Materials
- Fluid Flow and Transfer Processes

### これを引用

*IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamicsa*(巻 79, pp. 283-294). (Fluid Mechanics and its Applications; 巻数 79).

**Linear and nonlinear instability of a vortex ring.** / Fukumoto, Yasuhide; Hattori, Yuji.

研究成果: 著書/レポートタイプへの貢献 › 章

*IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamicsa.*巻. 79, Fluid Mechanics and its Applications, 巻. 79, pp. 283-294.

}

TY - CHAP

T1 - Linear and nonlinear instability of a vortex ring

AU - Fukumoto, Yasuhide

AU - Hattori, Yuji

PY - 2006

Y1 - 2006

N2 - A new linear instability mechanism of curvature origin is established for a vortex ring. The curvature effect reduces O(2) × SO(2) symmetry of a circularcylindrical tube to O(2), and fuels a pair of Kelvin waves whose azimuthal wavenumbers on the core are separated by one. For Kelvin's vortex ring, the growth rate and eigenfunctions are written out in closed form. In the inviscid case, the curvature effect dominates over the elliptically straining effect, but the former suffers from enhanced viscous damping. There are numerous excitable modes. As a first step toward an understanding of the route to a matured stage, we derive equations for weakly nonlinear evolution of amplitudes of the curvature instability. Our direct numerical simulation successfully captures the elliptical instability.

AB - A new linear instability mechanism of curvature origin is established for a vortex ring. The curvature effect reduces O(2) × SO(2) symmetry of a circularcylindrical tube to O(2), and fuels a pair of Kelvin waves whose azimuthal wavenumbers on the core are separated by one. For Kelvin's vortex ring, the growth rate and eigenfunctions are written out in closed form. In the inviscid case, the curvature effect dominates over the elliptically straining effect, but the former suffers from enhanced viscous damping. There are numerous excitable modes. As a first step toward an understanding of the route to a matured stage, we derive equations for weakly nonlinear evolution of amplitudes of the curvature instability. Our direct numerical simulation successfully captures the elliptical instability.

UR - http://www.scopus.com/inward/record.url?scp=84859832868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859832868&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:84859832868

SN - 9781402041808

VL - 79

T3 - Fluid Mechanics and its Applications

SP - 283

EP - 294

BT - IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamicsa

ER -