Linear instability characteristics of incompressible coaxial jets

The present study deals with the local linear instability of axisymmetric coaxial jets with a duct wall separating the two streams. The flow is assumed to be locally parallel, inviscid and incompressible. The objective of the work is to understand how the various parameters describing this flow geometry (i.e. boundary layers thicknesses at the exit, velocity ratio, wall thickness) may influence the instability of the flow and, in particular, the convective/absolute instability transition. A specific family of profiles is chosen for the modelling of the mean undisturbed flow and a spatial stability analysis is performed in order to identify the unstable modes and to assess how they are affected by the wake region behind the wall. An absolutely unstable mode is found, and its characteristics, depending on the velocity ratio and shear layers thicknesses, are determined. Results show that the absolute unstable mode is present only for a limited range of velocity ratios and that the corresponding frequency is almost constant if normalized with the mean velocity and wake thickness. This frequency value and the extension of the range of velocity ratios is similar to those found in the experiments on a similar geometry. Finally, a specific velocity ratio is found that maximizes the region at the jet exit for which an absolute instability behind the wall is present. This may increase the possibility for the onset of a global mode that may sustain the instability of the whole jet, enhancing considerably the mixing and entrainment characteristics between the two streams.