### Abstract

The effects of axial flow on the stability of a helical vortex tube are studied by short-wavelength stability analysis. By axial flow we mean the flow along the helical tube inside the vortex core. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube. The exponential growth rate is obtained analytically as the magnitude of the sum of three O(ε) and five O(ε2) complex numbers, where ε is the ratio of the core to curvature radius. At O(ε) the effect of axial flow can be regarded as the effect of the Coriolis force; as a result the instability is the superposition of the curvature instability and the Coriolis or precessional instability since the two instabilities occur under the same resonance condition. At O(ε2) combined effects of the axial flow and the torsion appear; the maximum growth rate increases when the period of particle motion increases.

Original language | English |
---|---|

Article number | 054102 |

Journal | Physics of Fluids |

Volume | 24 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*24*(5), [054102]. https://doi.org/10.1063/1.4717769

**Effects of axial flow on the stability of a helical vortex tube.** / Hattori, Y.; Fukumoto, Yasuhide.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 24, no. 5, 054102. https://doi.org/10.1063/1.4717769

}

TY - JOUR

T1 - Effects of axial flow on the stability of a helical vortex tube

AU - Hattori, Y.

AU - Fukumoto, Yasuhide

PY - 2012/5/1

Y1 - 2012/5/1

N2 - The effects of axial flow on the stability of a helical vortex tube are studied by short-wavelength stability analysis. By axial flow we mean the flow along the helical tube inside the vortex core. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube. The exponential growth rate is obtained analytically as the magnitude of the sum of three O(ε) and five O(ε2) complex numbers, where ε is the ratio of the core to curvature radius. At O(ε) the effect of axial flow can be regarded as the effect of the Coriolis force; as a result the instability is the superposition of the curvature instability and the Coriolis or precessional instability since the two instabilities occur under the same resonance condition. At O(ε2) combined effects of the axial flow and the torsion appear; the maximum growth rate increases when the period of particle motion increases.

AB - The effects of axial flow on the stability of a helical vortex tube are studied by short-wavelength stability analysis. By axial flow we mean the flow along the helical tube inside the vortex core. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube. The exponential growth rate is obtained analytically as the magnitude of the sum of three O(ε) and five O(ε2) complex numbers, where ε is the ratio of the core to curvature radius. At O(ε) the effect of axial flow can be regarded as the effect of the Coriolis force; as a result the instability is the superposition of the curvature instability and the Coriolis or precessional instability since the two instabilities occur under the same resonance condition. At O(ε2) combined effects of the axial flow and the torsion appear; the maximum growth rate increases when the period of particle motion increases.

UR - http://www.scopus.com/inward/record.url?scp=84861993161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861993161&partnerID=8YFLogxK

U2 - 10.1063/1.4717769

DO - 10.1063/1.4717769

M3 - Article

AN - SCOPUS:84861993161

VL - 24

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

M1 - 054102

ER -