scholarly journals Motion of a vortex filament with axial flow in the half space

2014 ◽  
Vol 31 (6) ◽  
pp. 1311-1335
Author(s):  
Masashi Aiki ◽  
Tatsuo Iguchi
Keyword(s):  
Half Space ◽  
Axial Flow ◽  
Vortex Filament

Slender-body analysis of the motion and stability of a vortex filament containing an axial flow

1971 ◽  
Vol 50 (2) ◽  
pp. 335-353 ◽  
Author(s):  
Sheila E. Widnall ◽  
Donald B. Bliss
Keyword(s):  
Travelling Waves ◽  
Stability Boundary ◽  
Axial Flow ◽  
Vortex Pair ◽  
Force Balance ◽  
Slender Body ◽  
Vortex Filament ◽  
Core Radius ◽  
Single Filament ◽  
The Stability

Previous results concerning the effects of axial velocity on the motion of vortex filaments are reviewed. These results suggest that a slender-body force balance between the Kutta–Joukowski lift on the vortex cross-section and the momentum flux within the curved filament will give some insight into the behaviour of the filament. These simple ideas are exploited for both a single vortex filament and a vortex pair, both containing axial flow. The stability of a straight vortex filament containing an axial flow to long wave sinusoidal displacements of its centre-line is investigated and the stability boundary obtained. The effect of axial flow on the stability of a vortex pair is explored. It is shown that to lowest order (in the ratio of vortex core radius to distance between the vortices) the effect of axial flow is to reduce the self-induced rotation of a single filament and that this effect can be considered as a change in effective core radius. To the next order, travelling waves appear in the instability, the instability mode for the vortex pair becomes non-planar but the amplification rate of the instability is not affected.

N-Solitons on a Curved Vortex Filament with Axial Flow

1988 ◽  
Vol 57 (10) ◽  
pp. 3365-3370 ◽  
Author(s):  
Takeshi Miyazaki ◽  
Yasuhide Fukumoto
Keyword(s):  
Axial Flow ◽  
Vortex Filament

Solitons on a vortex filament with axial flow

1992 ◽  
Vol 2 (3) ◽  
pp. 237-250 ◽  
Author(s):  
Kimiaki Konno ◽  
Yoshi H. Ichikawa
Keyword(s):  
Axial Flow ◽  
Vortex Filament

The instability of a straight vortex filament in a strain field

1975 ◽  
Vol 346 (1646) ◽  
pp. 413-425 ◽  
Keyword(s):  
Plane Strain ◽  
Cross Section ◽  
Strain Field ◽  
Narrow Band ◽  
Axial Flow ◽  
Mirror Image ◽  
Vortex Filament ◽  
Instability Mechanism ◽  
Helical Wave

A straight infinite vortex of finite cross section is deformed by the action of weak irrotational plane strain. The deformed vortex is shown, in the absence of axial flow, to be unstable to disturbances whose axial wavelengths lie in a narrow band, whose width is proportional to the imposed strain. The band is centred on the wavelength of the helical wave which does not propagate on the unstrained circular vortex. Thus support is given to the instability mechanism proposed recently by Widnall, Bliss & Tsai (1974). The argument depends, however, on the mirror image of the helical wave also being a possible non-propagating disturbance on the unstrained vortex.

scholarly journals Motion of a vortex filament in the half-space

2012 ◽  
Vol 75 (13) ◽  
pp. 5180-5185 ◽  
Author(s):  
Masashi Aiki ◽  
Tatsuo Iguchi
Keyword(s):  
Half Space ◽  
Vortex Filament

scholarly journals The motion of a buoyant vortex filament

2018 ◽  
Vol 857 ◽  
Author(s):  
Ching Chang ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Analytic Solution ◽  
Axial Flow ◽  
External Pressure ◽  
Transverse Component ◽  
Tangential Component ◽  
Force Balance ◽  
Vortex Filament ◽  
Vortex Rings ◽  
Asymptotic Model ◽  
Vortex Element

We investigate the motion of a thin vortex filament in the presence of buoyancy. The asymptotic model of Moore & Saffman (Phil. Trans. R. Soc. Lond.A, vol. 272, 1972, pp. 403–429) is extended to take account of buoyancy forces in the force balance on a vortex element. The motion of a buoyant vortex is given by the transverse component of force balance, while the tangential component governs the dynamics of the structure in the core. We show that the local acceleration of axial flow is generated by the external pressure gradient due to gravity. The equations are then solved for vortex rings. An analytic solution for a buoyant vortex ring at a small initial inclination is obtained and asymptotically agrees with the literature.

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