A temporal linear stability analysis of an inviscid incompressible swirling gas jet injected into a co-flowing liquid was conducted. The ratio of the tangential velocity to the axial velocity (swirl number) played a significant role in the destabilization of the gas jet. Even at small gas Weber numbers, the presence of swirl caused the higher order azimuthal modes to become unstable; the growth rates, and the dominant and limiting wave numbers of the higher order modes were greater than those of the varicose and sinuous modes. The differences in growth rates, limiting and dominant wave numbers of the various azimuthal modes became significant at large gas Weber numbers. An increase in liquid viscosity resulted in a reduction in the growth rates and the dominant wave numbers. The liquid co-flow velocity controlled the phase velocity of the unstable modes.

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