Elliptical instability of the Moore-Saffman model for a trailing wingtip vortex

Abstract eng:
In this study, the elliptical instability exhibited by two counter-rotating trailing vortices is considered. This type of vortex instability can be viewed as a resonance between two normal modes of a vortex and an externally imposed strain field. Recently, numerical investigations have extended earlier results that ignored axial flow to include models with a simple axial jet such as the similarity solution found by Batchelor [1]. Here, we present growth rates of elliptical instability for a family of velocity profiles found by Moore & Saffman [2]. These profiles involve a parameter n that depends on the wing loading, and are therefore capable of modelling both the jet-like and wake-like axial flow present in a trailing vortex at short and intermediate distances behind the wingtip. A direct numerical simulation is performed using an efficient spectral method in cylindrical coordinates developed by Matsushima & Marcus [3]. We compare our results to those for the Batchelor vortex.

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