Stability of symmetric vortices in two dimensions and over three-dimensional slender conical bodies

A general stability condition for vortices in a two-dimensional incompressible inviscid flow field is presented. This condition is first applied to analyse the stability of symmetric vortices behind elliptic cylinders and circular cylinders with a splitter plate at the rear stagnation point. The eff...

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Bibliographic Details
Published in:Journal of fluid mechanics 2003-04, Vol.480, p.65-94, Article S0022112002003567
Main Authors: CAI, JINSHENG, LIU, FENG, LUO, SHIJUN
Format: Article
Language:English
Subjects:
Asymmetry
Exact sciences and technology
Fluid dynamics
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Inviscid flows with vorticity
Inviscid instability
Laminar flows
Physics
Symmetry
Vortices
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Summary:A general stability condition for vortices in a two-dimensional incompressible inviscid flow field is presented. This condition is first applied to analyse the stability of symmetric vortices behind elliptic cylinders and circular cylinders with a splitter plate at the rear stagnation point. The effect of the size of the splitter plate on the stability of the vortices is studied. It is also shown that no stable symmetric vortices exist behind two-dimensional bodies based on the stability condition. The two-dimensional stability condition is then extended to analyse the absolute (temporal) stability of a symmetric vortex pair over three-dimensional slender conical bodies. The three-dimensional problem is reduced to a vortex stability problem for a pair of vortices in two dimensions by using the conical flow assumption, classical slender-body theory, and postulated separation positions. The bodies considered include circular cones and highly swept flat-plate wings with and without vertical fins, and elliptic cones of various eccentricities. There exists an intermediate cone with a finite thickness ratio between the circular cone and the flat-plate delta wing for which the symmetric vortices change from being unstable to being stable at a given angle of attack. The effects of the fin height and the separation position on the stability of the vortices are studied. Results agree well with known experimental observations.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112002003567