### Abstract

The three-dimensional motion of a flat uniform vortex sheet slightly perturbed initially in both streamwise and spanwise directions is studied on the basis of a Lagrangian representation of the motion. The vortex sheet at time t is represented as [formula ommited] where λ1 and λ2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. The behaviour of An,0 and An,1 is studied by an asymptotic analysis valid at large t. The analysis shows that singularity appears on the sheet at a critical time O (In ([formula omitted])), where ∊1 is the initial amplitude of the streamwise disturbance. The singularity is such that An,0 behaves like [formula omitted] while An,1 behaves like [formula omitted], for large n. The latter is associated with the vortex stretching intrinsic in three-dimensional dynamics of the sheet.

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

Pages (from-to) | 388-392 |

Number of pages | 5 |

Journal | Journal of the Physical Society of Japan |

Volume | 63 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1994 |

Externally published | Yes |

### Fingerprint

### Keywords

- singularity
- three-dimensionality
- vortex sheet
- vortex stretching

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Spontaneous Singularity Formation in the Shape of Vortex Sheet in Three-Dimensional Flow.** / Ishihara, Takashi; Kaneda, Yukio.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 63, no. 2, pp. 388-392. https://doi.org/10.1143/JPSJ.63.388

}

TY - JOUR

T1 - Spontaneous Singularity Formation in the Shape of Vortex Sheet in Three-Dimensional Flow

AU - Ishihara, Takashi

AU - Kaneda, Yukio

PY - 1994/1/1

Y1 - 1994/1/1

N2 - The three-dimensional motion of a flat uniform vortex sheet slightly perturbed initially in both streamwise and spanwise directions is studied on the basis of a Lagrangian representation of the motion. The vortex sheet at time t is represented as [formula ommited] where λ1 and λ2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. The behaviour of An,0 and An,1 is studied by an asymptotic analysis valid at large t. The analysis shows that singularity appears on the sheet at a critical time O (In ([formula omitted])), where ∊1 is the initial amplitude of the streamwise disturbance. The singularity is such that An,0 behaves like [formula omitted] while An,1 behaves like [formula omitted], for large n. The latter is associated with the vortex stretching intrinsic in three-dimensional dynamics of the sheet.

AB - The three-dimensional motion of a flat uniform vortex sheet slightly perturbed initially in both streamwise and spanwise directions is studied on the basis of a Lagrangian representation of the motion. The vortex sheet at time t is represented as [formula ommited] where λ1 and λ2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. The behaviour of An,0 and An,1 is studied by an asymptotic analysis valid at large t. The analysis shows that singularity appears on the sheet at a critical time O (In ([formula omitted])), where ∊1 is the initial amplitude of the streamwise disturbance. The singularity is such that An,0 behaves like [formula omitted] while An,1 behaves like [formula omitted], for large n. The latter is associated with the vortex stretching intrinsic in three-dimensional dynamics of the sheet.

KW - singularity

KW - three-dimensionality

KW - vortex sheet

KW - vortex stretching

UR - http://www.scopus.com/inward/record.url?scp=21344482236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344482236&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.63.388

DO - 10.1143/JPSJ.63.388

M3 - Article

AN - SCOPUS:21344482236

VL - 63

SP - 388

EP - 392

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 2

ER -