# 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…

## 4 Citations

### Leapfrogging criteria for a line vortex pair external to a circular cylinder

- PhysicsPhysics of Fluids
- 2020

The interaction of two line vortices of differing strengths in the presence of a circular cylinder is considered. Explicit criteria are derived, a function of vortex strengths (including strengths of…

### Collinear interaction of vortex pairs with different strengths—Criteria for leapfrogging

- Physics
- 2020

We formulate a system of equations that describe the motion of four vortices made up of two interacting vortex pairs, where the absolute strengths of the pairs are different. Each vortex pair moves…

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