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 |
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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.
In: Journal of the Physical Society of Japan, Vol. 63, No. 2, 01.01.1994, p. 388-392.Research output: Contribution to journal › Article
}
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 -