Abstract
Elliptical flows are of interest since they appear in various vortical flows in which circular vortices are deformed by straining flow. We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the evolution of bending waves is considered. Nonlinear interaction of the two base Kelvin waves results in cubic nonlinear terms, which leads to saturation of the elliptical instability. Next, the secondary instability is considered. Three Kelvin waves, one of which is a bending wave, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the previous numerical results on the secondary instability obtained by Kerswell J. Fluid Mech., 382, pp. 283-386, 1999.
| Original language | English |
|---|---|
| Title of host publication | Fluid Structure Interaction and Moving Boundary Problems IV |
| Pages | 193-201 |
| Number of pages | 9 |
| DOIs | |
| Publication status | Published - Dec 1 2007 |
| Event | 4th International Conference on Fluid Structure Interaction (Incorporating the Free and Moving Boundary Problems Seminar) - , United Kingdom Duration: May 14 2007 → May 16 2007 |
Publication series
| Name | WIT Transactions on the Built Environment |
|---|---|
| Volume | 92 |
| ISSN (Print) | 1743-3509 |
Other
| Other | 4th International Conference on Fluid Structure Interaction (Incorporating the Free and Moving Boundary Problems Seminar) |
|---|---|
| Country | United Kingdom |
| Period | 5/14/07 → 5/16/07 |
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All Science Journal Classification (ASJC) codes
- Architecture
- Civil and Structural Engineering
- Building and Construction
- Automotive Engineering
- Safety, Risk, Reliability and Quality
- Arts and Humanities (miscellaneous)
- Transportation
- Safety Research
- Computer Science Applications
Cite this
Instability of an elliptical flow : Weakly nonlinear analysis. / Hattori, Y.; Fukumoto, Yasuhide; Fujimura, K.
Fluid Structure Interaction and Moving Boundary Problems IV. 2007. p. 193-201 (WIT Transactions on the Built Environment; Vol. 92).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Instability of an elliptical flow
T2 - Weakly nonlinear analysis
AU - Hattori, Y.
AU - Fukumoto, Yasuhide
AU - Fujimura, K.
PY - 2007/12/1
Y1 - 2007/12/1
N2 - Elliptical flows are of interest since they appear in various vortical flows in which circular vortices are deformed by straining flow. We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the evolution of bending waves is considered. Nonlinear interaction of the two base Kelvin waves results in cubic nonlinear terms, which leads to saturation of the elliptical instability. Next, the secondary instability is considered. Three Kelvin waves, one of which is a bending wave, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the previous numerical results on the secondary instability obtained by Kerswell J. Fluid Mech., 382, pp. 283-386, 1999.
AB - Elliptical flows are of interest since they appear in various vortical flows in which circular vortices are deformed by straining flow. We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the evolution of bending waves is considered. Nonlinear interaction of the two base Kelvin waves results in cubic nonlinear terms, which leads to saturation of the elliptical instability. Next, the secondary instability is considered. Three Kelvin waves, one of which is a bending wave, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the previous numerical results on the secondary instability obtained by Kerswell J. Fluid Mech., 382, pp. 283-386, 1999.
UR - http://www.scopus.com/inward/record.url?scp=38849092562&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38849092562&partnerID=8YFLogxK
U2 - 10.2495/FSI070181
DO - 10.2495/FSI070181
M3 - Conference contribution
AN - SCOPUS:38849092562
SN - 9781845640729
T3 - WIT Transactions on the Built Environment
SP - 193
EP - 201
BT - Fluid Structure Interaction and Moving Boundary Problems IV
ER -