Axisymmetric and flapping global instabilities of M = 1 jets

The instabilities of a perfectly expanded jet at M = 1 are investigated by means of global analysis. Two configurations are considered and compared. A reference setup includes the convergent nozzle within the computational domain. A modeled setup is used to indirectly model the effect of the nozzle on the flow. Both configurations are found to be globally unstable, indicative of the presence of an absolute instability mechanism. The results ascribe the generation of the absolute instability to the instantaneous transformation of the boundary layer within the nozzle into a rapidly expanding free shear layer past the nozzle exit. The constraining effect of the nozzle walls in the reference configuration leads to a lower instability growth rate than in the modeled case. The eigenfunctions are split into upstream-and downstream-Traveling parts, and decomposed into vortical, acoustic and thermal components using momentum potential theory. The leading axisymmetric and flapping modes are found to have a common structure. In the reference setup, the eigenfunctions consist of upstream-Traveling acoustic waves and downstream-Traveling Kelvin-Helmholtz modes. In the modeled setup, the eigenfunctions are concentrated at the location of the rapidly expanding shear layer.