Direct numerical simulations of the elliptic instability of a vortex pair

The objective of this study is to perform direct numerical simulations (DNS) of the three-dimensional short-wavelength elliptic instability developing in a counter-rotating vortex pair, and to reproduce numerically a water-tank experiment. The main features of the elliptic instability are recovered by the simulations. In particular, the spatial structure and the temporal evolution of the most amplified perturbation mode during the linear regime correspond to both experimental measurements and theoretical predictions. The long-term evolution is also simulated, and the stages leading to transition to turbulence are described. Some elements resulting from simulations related to the interaction between the short-wavelength elliptic instability and the long-wavelength Crow instability are provided.