Global oscillations in low-density round jets with parabolic velocity profiles

Abstract

Experiments and spatiotemporal stability analysis are carried out to study the global oscillations in laminar low-density round jets with parabolic velocity profiles. The experimental results of laminar low-density jets with parabolic velocity profiles exhibit global axisymmetric oscillations. The spatiotemporal stability results based on base profiles from numerical simulations are consistent with the present experimental results. These results differ from the prediction of stability study by Coenen et al. (Phys. Fluids, vol. 20, 2008, p. 074104). They reported that the low-density jets with near parabolic velocity profiles show global helical oscillations. It is observed that the method used by Coenen et al. is not able to predict the nature of global oscillations observed in experiments for low-density jets with near parabolic profiles. The present spatiotemporal stability results demonstrate that the base flows from Navier–Stokes equations are required to predict the critical conditions observed in experiments for low-density jets with near parabolic velocity profiles. The breakdown distance of globally unstable low-density jets scales with $(Re-Re_c)^{-1/2}$ ( $Re_c$ is the critical Reynolds number), consistent with the scaling law obtained from the nonlinear global mode of the Ginzburg–Landau equation.