Skip to main content Accessibility help

Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction

  • K. OBERLEITHNER (a1), M. SIEBER (a1), C. N. NAYERI (a1), C. O. PASCHEREIT (a1), C. PETZ (a2), H.-C. HEGE (a2), B. R. NOACK (a3) and I. WYGNANSKI (a4)...


The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.


Corresponding author

Email address for correspondence:


Hide All
Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183219.
Cabral, B. & Leedom, L. C. 1993 Imaging vector fields using line integral convolution. In Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), Anaheim, CA, pp. 263270.
Cantwell, B. J. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13, 457515.
Chigier, N. & Chervinsky, A. 1965 Experimental and theoretical study of turbulent swirling jets issuing from a round orifice. Isr. J. Technol. 4, 4454.
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.
Cohen, J., Marasli, B. & Levinski, V. 1994 Interaction between the mean flow and coherent structures in turbulent mixing layers. J. Fluid Mech. 260, 8194.
Cohen, J. & Wygnanski, I. 1987 The evolution of instabilities in the axisymmetric jet. Part I. The linear growth of disturbances near the nozzle. Part II. The flow resulting from the interaction between two waves. J. Fluid Mech. 176, 191219.
Crighton, D. G. & Gaster, M. 1976 Stability of slowly diverging jet flow. J. Fluid Mech. 77, 397413.
Depardon, S., Lasserre, J. J., Brizzi, L. E. & Borée, J. 2007 Automated topology classification method for instantaneous velocity fields. Exp. Fluids 42, 697710.
Duwig, C. & Fuchs, L. 2007 Large eddy simulation of vortex breakdown/flame interaction. Phys. Fluids 19, 5103.
Escudier, M. P. & Keller, J. J. 1985 Recirculation in swirling flow. A manifestation of vortex breakdown. AIAA J. 23, 111116.
Faler, J. H. & Leibovich, S. 1978 An experimental map of the internal structure of a vortex breakdown. J. Fluid Mech. 86, 313335.
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683704.
Gallaire, F. & Chomaz, J.-M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223253.
Gallaire, F., Chomaz, J.-M. & Huerre, P. 2004 Closed-loop control of vortex breakdown: a model study. J. Fluid Mech. 511, 6793.
Gallaire, F., Rott, S. & Chomaz, J.-M. 2004 Experimental study of a free and forced swirling jet. Phys. Fluids 16, 29072917.
Gallaire, F., Ruith, M., Meiburg, E., Chomaz, J.-M. & Huerre, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 7180.
Gaster, M. 1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723727.
Gaster, M. 1974 On the effects of boundary-layer growth on flow stability. J. Fluid Mech. 66, 465480.
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 2339.
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365424.
Holmes, P., Lumley, J. L. & Berkooz, G. 1998 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.
Hussain, A. K. M. F. & Reynolds, W. C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241258.
Juniper, M. P., Li, L. K. & Nichols, J. W. 2009 Forcing of self-excited round jet diffusion flames. Proc. Combust. Inst. 32 (1), 11911198.
Khorrami, M. R. 1991 On the viscous modes of instability of a trailing line vortex. J. Fluid Mech. 225, 197212.
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 (1), 206229.
Lambourne, N. C. & Bryer, D. W. 1962 The bursting of leading-edge vortices: some observations and discussion of the phenomenon, Tech. Rep. Ministry of Aviation, Aeronautical Research Council, vol. 3282.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Laufer, J. 1975 New trends in experimental turbulence research. Annu. Rev. Fluid Mech. 7, 307326.
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115159.
Liu, J. 1989 Coherent structures in transitional and turbulent free shear flows. Annu. Rev. Fluid Mech. 21, 285315.
Ludwieg, H. 1961 Ergänzung zu der Arbeit: Stabilität der Strömung in einem zylindrischen Ringraum. Z. Flugwiss. 9, 359.
Lumley, J. L. 1967 Atmospheric Turbulence and Radio Wave Propagation. Elsevier.
Malik, M. R., Zang, T. A. & Hussaini, M. Y. 1985 A spectral collocation method for the Navier–Stokes equations. J. Comput. Phys. 61, 6488.
Martinelli, F., Olivani, A. & Coghe, A. 2007 Experimental analysis of the precessing vortex core in a free swirling jet. Exp. Fluids 42, 841841.
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521544.
Michalke, A. 1999 Absolute inviscid instability of a ring jet with back-flow and swirl. Eur. J. Mech. 18, 312.
Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 120.
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911916.
Noack, B. R., Afanasiev, K., Morzyński, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335363.
Oberleithner, K., Lück, M., Paschereit, C. O. & Wygnanski, I. 2009 Control of vortex breakdown in critical swirl regime using azimuthal forcing. In Minnowbrook VI, Syracuse University.
Olendraru, C. & Sellier, A. 2002 Viscous effects in the absolute convective instability of the Batchelor vortex. J. Fluid Mech. 459, 371396.
Panda, J. & McLaughlin, D. K. 1994 Experiments on the instabilities of a swirling jet. Phys. Fluids 6, 263276.
Parras, L. & Fernandez-Feria, R. 2007 Spatial stability and the onset of absolute instability of Batchelor's vortex for high swirl numbers. J. Fluid Mech. 583, 27.
Pier, B. & Huerre, P. 2001 Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145174.
Plaschko, P. 1979 Helical instabilities of slowly divergent jets. J. Fluid Mech. 92, 209215.
Provansal, M., Mathis, C. & Boyer, L. 1987 Benard-von Karman instability: transient and forced regimes. J. Fluid Mech. 182, 122.
Rajaratnam, N. 1976 Turbulent Jets (Developments in Water Science, vol 5). Elsevier.
Roshko, A. 1977 Errata: structure of turbulent shear flows: a new look. AIAA J. 15, 768768.
Rowley, C. 2005 Model reduction for fluids using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15 (3), 9971013.
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115.
Ruith, M. R., Chen, P., Meiburg, E. & Maxworthy, T. 2003 Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation. J. Fluid Mech. 486, 331378.
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545559.
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 528.
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I. Coherent structures. Q. Appl. Math. XLV, 561571.
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7, 309317.
Stalling, D. & Hege, H.-C. 1995 Fast and resolution independent line integral convolution. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (SIGGRAPH), Los Angeles, CA, pp. 249256.
Stuart, J. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 121.
Townsend, A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
VanDyke, M. Dyke, M. 1975 Perturbation Methods in Fluid Mechanics, annotated edn. The Parabolic Press.
Weisbrot, I. & Wygnanski, I. 1988 On coherent structures in a highly excited mixing layer. J. Fluid Mech. 195, 137.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction

  • K. OBERLEITHNER (a1), M. SIEBER (a1), C. N. NAYERI (a1), C. O. PASCHEREIT (a1), C. PETZ (a2), H.-C. HEGE (a2), B. R. NOACK (a3) and I. WYGNANSKI (a4)...


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.