Stability Analysis of Round Jets with Density Gradient

Using Chebyshev spectral collocation method, the temporal and spatial stability analysis of a round jet with tangential velocity profile and transverse density gradient is carried out. The characteristic frequencies, wave numbers and eigen modes of the most unstable normal perturbations are analyzed. It is concluded that considering transverse density gradient in most cases leads to decrease in the growth rates and phase velocities of all unstable modes. It is shown that the relations between the phase and group velocities obtained from the temporal and spatial stability analysis of round jet turn out to be valid only for large shear layer thicknesses.