Local stability analysis of an inviscid transverse jet

A local linear stability analysis is performed for a round inviscid jet with constant density that is injected into a uniform crossflow of the same density. The baseflow is obtained from a modified version of the inviscid transverse jet near-field solution of Coelho & Hunt (J. Fluid Mech. vol. 200, 1989, p. 95) which is valid for small values of the crossflow-to-jet velocity ratio λ. A Fourier expansion in the azimuthal direction is used to couple the disturbances with the three-dimensional crossflow. The spatial growth rates of the modes corresponding to the axisymmetric and first helical modes of the free jet as λ → 0 increase as λ increases. The diagonal dominance of the dispersion relation matrix is used as a quantitative criterion to estimate the range of velocity ratios (0 < λ < λc) within which the transverse jet instability can be considered to have a structure similar to that of the free jet. Further, we show that for λ>0 positive and negative helical modes have different growth rates, suggesting an inherent weak asymmetry in the transverse jet.