Stability of leapfrogging vortex pairs: A semi-analytic approach

@article{Behring2019StabilityOL,
  title={Stability of leapfrogging vortex pairs: A semi-analytic approach},
  author={Brandon Behring and Roy H. Goodman},
  journal={Physical Review Fluids},
  year={2019}
}
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as `leapfrogging' orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W.\ Grobli (1877) and A.\ E.\ H.\ Love (1883), and can be parameterized by a dimensionless parameter $\alpha$ related to the geometry of the initial configuration. Simulations by Acheson (2000) and numerical Floquet analysis by Tophoj and Aref (2012) both… 
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