1. Resonant instability in two-dimensional vortex arrays by Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proceedings A Volume 467(2128):1164-1185 April 8, 2011 ©2011 by The Royal Society

2. Possible eigenvalue behaviour for (a) an exchange of stability (giving rise to a non-propagating unstable eigenmode), and (b) a Hamiltonian Hopf bifurcation (leading to an oscillatory instability). Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

3. Schematic of perturbations involving (a) a displacement or (b) deformation of the vortex cores. m denotes the azimuthal wavenumber of the perturbation. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

4. Perturbation involving an overall displacement of the configuration, schematically illustrated through the case of a co-rotating vortex pair. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

5. Schematic of possible phase relations between disturbances on three vortices. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

6. (a) Angular velocity for the elliptical model (dashed line) and the full solution (solid line) for three identical co-rotating vortices. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

7. Selected eigenvalues for three co-rotating vortices, showing the prediction for the development of the first resonance from the elliptical model (a), together with results from an accurate linear stability analysis (b). Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

8. Eigenvalues for three co-rotating vortices. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

9. Close-up view of the second resonance occurring for three vortices. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society

10. Imaginary part of the overall-displacement eigenvalue σI and of the angular velocity Ω of the configuration. Paolo Luzzatto-Fegiz, and Charles H. K. Williamson Proc. R. Soc. A 2011;467:1164-1185 ©2011 by The Royal Society