Elliptic Instability of Counter-Rotating Vortices: Experiment and Direct Numerical Simulation

Abstract

The short-wavelength elliptic instability of a pair of closely spaced counter-rotating vortices is analyzed using water tank experiments and direct numerical simulations. Qualitative and quantitative comparison shows excellent agreement and validates each of these complementary approaches. Both sets of results are used to give a detailed description of the instability characteristics. In the initial phase, the vortices are subject to a three-dimensional perturbation of their internal structure, with a wavelength scaling on the vortex core size and a distinct phase relationship between the two vortices. In the nonlinear evolution of the  ow, the growth of the perturbations leads to the generation of secondary vortices and the breakdown of the initial pair into small-scale turbulence, accompanied by a rapid decrease of the average circulation. The growth rate of the instability is found to be higher than the one of the well-known Crow instability. The interaction between both mechanisms is also investigated, and an even faster decay of circulation is observed than for the cases where each instability acts alone. The relevance of these results for realistic aircraft trailing wakes is discussed.