The instability of a vortex ring is studied by direct numerical simulation of the Navier-Stokes equations. First we consider a vortex ring in a periodic cylindrical domain. The Widnall instability of bending waves is observed clearly. Next we consider a vortex ring confined in a torus. A novel method for solving the Navier-Stokes equations with high accuracy in a torus is developed and used in the simulation. The curvature instability, which is found by the authors recently, is captured for the first time. The growth rate of unstable modes agrees well with the value obtained by linear stability analysis. The structure of destabilized vortex ring is investigated in detail.
Numerical Detection of a New Instability Mode of a Vortex Ring
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Hattori, Y, & Fukumoto, Y. "Numerical Detection of a New Instability Mode of a Vortex Ring." Proceedings of the ASME/JSME 2007 5th Joint Fluids Engineering Conference. Volume 1: Symposia, Parts A and B. San Diego, California, USA. July 30–August 2, 2007. pp. 1111-1118. ASME. https://doi.org/10.1115/FEDSM2007-37138
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