Skip to main content Accessibility help

Global stability of buoyant jets and plumes

  • R. V. K. Chakravarthy (a1), L. Lesshafft (a1) and P. Huerre (a1)


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.


Corresponding author

Email address for correspondence:


Hide All
Åkervik, E., Ehrenstein, U., Gallaire, F. & Henningson, D. 2008 Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. (B/Fluids) 27, 113.
Bharadwaj, K. & Das, D. 2017 Global instability analysis and experiments of buoyant plumes. J. Fluid Mech. 832, 97145.
Boujemaa, S., Amielh, M. & Chauve, M. P. 2004 Analyse spatio-temporelle de jets axisymétriques d’air et d’hélium. C. R. Méc. 332 (11), 933939.
Cetegen, B. M. & Kasper, K. D. 1996 Experiments on the oscillatory behavior of buoyant plumes of helium and helium-air mixtures. Phys. Fluids 8 (11), 29742984.
Chakravarthy, R. V. K.2015 Local and global instabilities in buoyant jets and plumes. PhD thesis, École Polytechnique, Palaiseau, France.
Chakravarthy, R. V. K., Lesshafft, L. & Huerre, P. 2015 Local linear stability of laminar axisymmetric plumes. J. Fluid Mech. 780, 344369.
Chandler, G. J.2010 Sensitivity analysis of low density jets and flames. PhD thesis, University of Cambridge, Cambridge, UK.
Chomaz, J.-M. 2003 Fully nonlinear dynamics of parallel wakes. J. Fluid Mech. 495, 5775.
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84 (2), 119144.
Coenen, W., Lesshafft, L., Garnaud, X. & Sevilla, A. 2017 Global instability of low-density jets. J. Fluid Mech. 820, 187207.
Colonius, T. 2004 Modeling artificial boundary conditions for compressible flow. Annu. Rev. Fluid Mech. 36, 315345.
Couairon, A. & Chomaz, J. M. 1997 Absolute and convective instabilities, front velocities and global modes in nonlinear systems. Physica D: Nonlinear Phenomena. 108 (3), 236276.
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013 Modal and transient dynamics of jet flows. Phys. Fluids 25 (4), 044103.
Hallberg, M. P. & Strykowski, P. J. 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493507.
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473537.
Jiang, X. & Luo, K. H. 2000 Direct numerical simulation of the puffing phenomenon of an axisymmetric thermal plume. Theor. Comput. Fluid Dyn. 14, 5574.
Khorrami, M. R., Malik, M. R. & Ash, R. L. 1989 Application of spectral collocation techniques to the stability of swirling flows. J. Comput. Phys. 81, 206229.
Lakkaraju, R. & Alam, M. 2007 Effects of Prandtl number and a new instability mode in a plane thermal plume. J. Fluid Mech. 592, 221231.
Lesshafft, L. 2015 Linear global stability of a confined plume. Theoret. Appl. Mech. Lett. 5 (3), 126128.
Lesshafft, L.2017 Artificial eigenmodes in truncated flow domains. Preprint, arXiv:1704.08450.
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19 (2), 024102.
Lesshafft, L., Huerre, P. & Sagaut, P. 2007 Frequency selection in globally unstable round jets. Phys. Fluids 19, 054108.
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393409.
Lesshafft, L. & Marquet, O. 2010 Optimal velocity and density profiles for the onset of absolute instability in jets. J. Fluid Mech. 662, 398408.
Lopez, J. M. & Marques, F. 2013 Instability of plumes driven by localized heating. J. Fluid Mech. 736, 616640.
Marquet, O. & Lesshafft, L.2015 Identifying the active flow regions that drive linear and nonlinear instabilities. Preprint, arXiv:1508.07620.
McMurtry, P. A., Jou, W. H., Riley, J. J. & Metcalfe, R. W. 1986 Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24 (6), 962970.
Mollendorf, J. C. & Gebhart, B. 1973 An experimental and numerical study of the viscous stability of a round laminar vertical jet with and without thermal buoyancy for symmetric and asymmetric perturbations. J. Fluid Mech. 61 (2), 367399.
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. Phys. Fluids 213, 611639.
Monkewitz, P. A. & Sohn, K. 1988 Absolute instability in hot jets. AIAA J. 26, 911916.
Nichols, J. W., Schmid, P. J. & Riley, J. J. 2007 Self-sustained oscillations in variable-density round jets. J. Fluid Mech. 582, 341376.
Riley, D. S. & Tveitereid, M. 1984 On the stability of an axisymmetric plume in a uniform flow. J. Fluid Mech. 142, 171186.
Satti, R. P. & Agrawal, A. K. 2006 Computational analysis of gravitational effects in low-density gas jets. AIAA 44 (7), 15051515.
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows, Applied Mathematical Sciences, vol. 142. Springer.
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 213, 309317.
Subbarao, E. R. & Cantwell, B. J. 1992 Investigation of a co-flowing buoyant jet: experiments on the effect of Reynolds number and Richardson number. J. Fluid Mech. 245, 6990.
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aero. Sci. 39 (4), 249315.
Tritton, D. J. 2012 Physical Fluid Dynamics. Springer Science & Business Media.
Wakitani, S. 1980 The stability of a natural convection flow above a point heat source. J. Phys. Soc. Japan 49 (6), 23922399.
Yih, C. S. 1988 Fluid Mechanics. West River Press.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed