The flow characteristics of an annular swirling liquid jet in a gas medium have been examined by direct solution of the compressible Navier-Stokes equations. A mathematical formulation is developed that is capable of representing the two-phase flow system while the volume of fluid method has been adapted to account for the gas compressibility. The effect of surface tension is captured by a continuum surface force model. Analytical swirling inflow conditions have been derived that enable exact definition of the boundary conditions at the domain inlet. The mathematical formulation is then applied to the computational analysis to achieve a better understanding on the flow physics by providing detailed information on the flow development. Fully 3D parallel direct numerical simulation (DNS) has been performed utilizing 512 processors, and parallelization of the code was based on domain decomposition. The numerical results show the existence of a recirculation zone further down the nozzle exit. Enhanced and sudden liquid dispersion is observed in the cross-stream wise direction with vortical structures developing at downstream locations due to Kelvin-Helmholtz instability. Downstream the flow becomes more energetic, and analysis of the energy spectra shows that the annular gas-liquid two-phase jet has a tendency of transition to turbulence.