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Title: Density and surface tension effects on vortex stability. Part 1. Curvature instability
The curvature instability of thin vortex rings is a parametric instability discovered from short-wavelength analysis by Hattori & Fukumoto ( Phys. Fluids , vol. 15, 2003, pp. 3151–3163). A full-wavelength analysis using normal modes then followed in Fukumoto & Hattori ( J. Fluid Mech. , vol. 526, 2005, pp. 77–115). The present work extends these results to the case with different densities inside and outside the vortex core in the presence of surface tension. The maximum growth rate and the instability half-bandwidth are calculated from the dispersion relation given by the resonance between two Kelvin waves of $m$ and $m+1$ , where $m$ is the azimuthal wavenumber. The result shows that vortex rings are unstable to resonant waves in the presence of density and surface tension. The curvature instability for the principal modes is enhanced by density variations in the small axial wavenumber regime, while the asymptote for short wavelengths is close to the constant density case. The effect of surface tension is marginal. The growth rates of non-principal modes are also examined, and long waves are most unstable.  more » « less
Award ID(s):
1706934
NSF-PAR ID:
10312404
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
913
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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