Stability of swirling coaxial jets

In order to improve the mixing properties of injectors, we investigate the potential synergy between azimuthal and axial shear. To this end, we examine the linear modal stability of a simplified analytical model which consists of a temporally evolving swirling jet surrounded by an annular jet with a different axial velocity. We denote $\Lambda = V_2/V_1$ the ratio between the axial velocity of the non-swirling outer jet $V_2$ and the axial velocity of the central jet $V_1$; and $q=\Omega_c r_1/V_1$ the swirl number of the central jet where $\Omega_c$ is the rotation rate on the axis and $r_1$ the central jet radius. The present study extends the results of Gallaire \& Chomaz (2003) where a single swirling jet was considered. For all values of the swirl number up to $q=2$, adding the outer non-swirling jet substantially increases the growth rate of the most amplified mode, which can be more than doubled when $\Lambda > 1$. This is the result of the collaborative axial and azimuthal shear instabilities localised in between the two jets. The mode selection of larger azimuthal wavenumbers with increasing $q$, identified by Gallaire \& Chomaz, is no longer observed when the outer jet is at least as fast as the central jet $\Lambda > 1$, the axisymmetric mode being the most amplified.