Hydrodynamic stability of a periodically unsteady swirling jet

The stability characteristics of a jet with a low-frequency time-dependent periodic swirl are determined. An analytical dispersion relation for the perturbations is obtained and solved numerically. Growth rates and celerities determined from this formulation are compared with predictions based on applying steady state analysis to instantaneous velocity profiles, i.e., the quasisteady approach. The results show that periodic unsteadiness in the swirl causes variations in the growth rates and celerities of the unstable modes. Furthermore, it is shown that the quasisteady approach is not applicable and fails to predict the magnitudes of these variations.