<p>The phenomenon of two-phase flow, where a liquid jet is issued from a central nozzle and atomised by the high-speed annular gas stream in a coaxial setup, is considered in this numerical study. The purpose of this paper is to investigate primary jet breakup and jet unsteadiness during the coaxial airblast atomization process. The present simulation aims to establish a better understanding of the flapping phenomenon of the liquid jet. In this work, jet instabilities were characterised at two different axial locations downstream of the atomiser exit. In addition to that, the turbulence statistics were analysed in a two-phase flow. Furthermore, the state of turbulence in the various regimes of the jet flow was studied using anisotropic invariant maps. The DDES (delayed detached eddy simulation) technique is adopted to compute the gas–liquid flow, while the volume of fluid technique is used to capture the gas–liquid interface. The simulation results have shown good qualitative and quantitative agreement with the in-house experimental observations. The influence of fluid flow through the central nozzle on the turbulence statistics is examined by comparing the current two-phase case with a hypothetical case, where air flows through the annular passage, and liquid flow through the central nozzle is absent.</p>