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Three-dimensional stability of a vortex pair

Abstract : This paper investigates the three-dimensional stability of the Lamb-Chaplygin vortex pair. Short-wavelength instabilities, both symmetric and antisymmetric, are found. The antisymmetric mode possesses the largest growth rate and is indeed the one reported in a recent experimental study [J. Fluid Mech. 360, 85 1998]. The growth rates, wave numbers of maximum amplification, and spatial eigenmodes of these short-wavelength instabilities are in good agreement with the predictions from elliptic instability theory. A long-wavelength symmetric instability similar to the Crow instability of a pair of vortex filaments is also recovered. Oscillatory bulging instabilities, both symmetric and antisymmetric, are identified albeit their growth rates are lower than for the short-wavelength instabilities. Their behavior and eigenmodes resemble those of the oscillatory bulging instability occurring in the mixing layer.
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Paul Billant, Pierre Brancher, Jean-Marc Chomaz. Three-dimensional stability of a vortex pair. Physics of Fluids, American Institute of Physics, 1999, vol. 11 (n° 8), pp. 2069-2077. ⟨10.1063/1.870069⟩. ⟨hal-01727550⟩

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