Elliptic instability in two-dimensional flattened Taylor-Green vortices

The aim of the present paper is to study three-dimensional elliptic instability in two-dimensional flattened Taylor-Green vortices, which constitutes a model problem for the topics of wake vortex dynamics. Shortwave asymptotics and classical linear stability theory are developed. Both approaches show that the flow is unstable. In particular, the structure of the most amplified growing mode is the same as that obtained in unbounded elliptical flows. The limits of the linear regime and the effects of the nonlinear interactions are characterized by means of a spectral Direct Numerical Simulation (DNS).