Global stability of buoyant jets and plumes

Abstract

The linear global stability of laminar buoyant jets and plumes is investigated under the low-Mach-number approximation. For Richardson numbers in the range $10^{-4}\leqslant Ri\leqslant 10^{3}$ and density ratios $S=\unicode[STIX]{x1D70C}_{\infty }/\unicode[STIX]{x1D70C}_{jet}$ between 1.05 and 7, only axisymmetric perturbations are found to exhibit global instability, consistent with experimental observations in helium jets. By varying the Richardson number over seven decades, the effects of buoyancy on the base flow and on the instability dynamics are characterised, and distinct behaviour is observed in the low-$Ri$ (jet) and in the high-$Ri$ (plume) regimes. A sensitivity analysis indicates that different physical mechanisms are responsible for the global instability dynamics in both regimes. In buoyant jets at low Richardson number, the baroclinic torque enhances the basic shear instability, whereas buoyancy provides the dominant instability mechanism in plumes at high Richardson number. The onset of axisymmetric global instability in both regimes is consistent with the presence of absolute instability. While absolute instability also occurs for helical perturbations, it appears to be too weak or too localised to give rise to a global instability.