In this paper we investigate by numerical simulations the evolution of three-dimensional perturbations on a rolling-up vortex sheet produced by a wing that flies at constant speed. The objective is to find mechanisms of energy growth that allow large amplification of energy at the wavelength of the Crow instability in the far field of the wake of aircrafts. A direct two-dimensional simulation of the vortex sheet shows that the flow spirals into two opposite trailing vortices. We first evaluate the end of the roll-up stage by comparing the distribution of vorticity in the vortices to that of a Lamb-Oseen vortex. Then a stability analysis of the steady trailing vortices indicates that the flow is unstable to the Crow instability. An optimal perturbation is used to investigate the mechanisms of energy growth in the rolling-up vortex sheet at the wavelength of previously characterized Crow instability. A mechanism at short time is found that corresponds to an Orr mechanism which is related to the mean shear in the vortex sheet and a large time mechanism is also observed that is related to the optimal amplification of the Crow instability by initial vorticity in the middle plane of the wake already investigated by Brion. 4.