A numerical study of a coaxial liquid jet sheared by an annular high-speed stream is performed at moderate density and velocity ratio between phases. The destabilization mechanism of the jet is studied : due to the shear induced by the high-speed stream, annular interfacial waves are generated near the jet injection, which subsequently connect and yield a sinuous organization for the whole jet, leading to a global flapping phenomenon. The influence of the high-speed stream boundary layer thickness on this flapping is investigated, as well as the influence of the velocity and the momentum flux ratio between phases. It appears that it is not sufficient to consider only the momentum flux ratio between phases to characterize the flapping dynamics or the steps of the atomization process. On the other hand, the Reynolds and Weber numbers based on the high-speed stream properties display a strong influence on these phenomena. (C) 2018 Elsevier Ltd. All rights reserved.