Inviscid axisymmetric absolute instability of swirling jets

Journal of Fluid Mechanics

Volumn 613, Issue , 2008, Pages 1-33

  Healey, J J ^a  

^a KEELE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CYLINDERS (SHAPES); DISPERSION (WAVES); QUANTUM THEORY; STABILITY; VELOCITY; VORTEX FLOW;

ABSOLUTE INSTABILITY; CENTRIFUGAL INSTABILITY; CRITICALITY CONDITION; DISPERSION RELATIONS; HOMOGENEOUS BOUNDARY CONDITION; PROPAGATION CHARACTERISTICS; SHEAR-LAYER THICKNESS; SUBCRITICAL TRANSITION;

SHEAR FLOW;

BOUNDARY CONDITION; JET FLOW; MODELING; SUPERCRITICAL FLOW; VELOCITY PROFILE; VORTEX FLOW;

EID: 53949093453     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008003236     Document Type: Article

References (53)

1. BATCHELOR, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20, 645-658.
2. BENJAMIN, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14, 593-629.
3. BENJAMIN, T. B. 1967 Some developments in the theory of vortex breakdown. J. Fluid Mech. 28, 65-84.
4. BENJAMIN, T. B. 1978 Bifurcation phenomena in steady flows of a viscous fluid I. Theory. Proc. R. Soc. Lond. A 359, 1-26.
5. BENJAMIN, T. B. & MULLIN, T. 1981 Anomalous modes in the Taylor experiment. Proc. R. Soc. Lond. A 377, 221-249.
6. BERAN, P. S. & CULICK, F. E. C. 1992 The role of non-uniqueness in the development of vortex breakdown in tubes. J. Fluid Mech. 242, 491-527.
7. BILLANT, P., CHOMAZ, J.-M. & HUERRE, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183-219.
8. BRIGGS, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.
9. COUAIRON, A. & CHOMAZ, J.-M. 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11, 3688-3703.
10. DELBENDE, I., CHOMAZ, J.-M. & HUERRE, P. 1998 Absolute/convective instabilities in the Batchelor vortex: A numerical study of the linear impulse response. J. Fluid Mech. 355, 229-254.
11. DRAZIN, P. G. & REID, W. H. 1981 Hydrodynamic Stability Theory Cambridge University Press.
12. ESCUDIER, M. P. 1984 Observations of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids 2, 189-196.
13. ESCUDIER, M. P., BORNSTEIN, J. & MAXWORTHY, T. 1982 The dynamics of confined vortices. Proc. R. Soc. Lond. A 382, 335-360.
14. GALLAIRE, F. & CHOMAZ, J.-M. 2003a Instability mechanisms in swirling flows. Phys. Fluids 15, 2622-2639.
15. GALLAIRE, F. & CHOMAZ, J.-M. 2003b Mode selection in swirling jet experiments: A linear stability analysis. J. Fluid Mech. 494, 223-253.
16. GALLAIRE, F. & CHOMAZ, J.-M. 2004 The role of boundary conditions in a simple model of incipient vortex breakdown. Phys. Fluids 16, 274-286.
17. GALLAIRE, F., RUITH, M., MEIBURG, E., CHOMAZ, J.-M. & HUERRE, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 71-80.
18. GASTER, M. 1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723-727.
19. GRABOWSKI, W. & BERGER, S. 1976 Solutions of the Navier-Stokes equations for vortex breakdown. J. Fluid Mech. 75, 525-544.
20. HARVEY, J. K. 1960 Analysis of the vortex breakdown phenomenon. Part II. Report no. 103, Aero. Dept., Imperial College.
21. HARVEY, J. K. 1962 Some observations of the vortex breakdown phenomenon. J. Fluid Mech. 14, 585-592.
22. HEALEY, J. J. 2005 Long-wave theory for a new convective instability with exponential growth normal to the wall. Phil. Trans. R. Soc. Lond. A 363, 1119-1130.
23. HEALEY, J. J. 2006a Inviscid long-wave theory for the absolute instability of the rotating-disk boundary layer. Proc. R. Soc. Lond. A 462, 1467-1492.
24. HEALEY, J. J. 2006b A new type of convective instability with exponential growth perpendicular to the basic flow. J. Fluid Mech. 560, 279-310.
25. HEALEY, J. J. 2007 Enhancing the absolute instability of a boundary layer by adding a far-away plate. J. Fluid Mech. 579 29-61.
26. HEALEY, J. J., BROOMHEAD, D. S., CLIFFE, K. A., JONES, R. & MULLIN, T. 1991 The origins of chaos in a modified van der Pol oscillator. Physica D 48, 322-339.
27. HOWARD, L. N. & GUPTA, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14 463-476.
28. HUERRE, P. & MONKEWITZ, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151-168.
29. HUERRE, P. & MONKEWITZ, P. A. 1990 Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473-537.
30. IVANIC, T., FOUCAULT, E. & PECHEUX, J. 2003 Dynamics of swirling jet flows. Exps. Fluids 35, 317-324.
31. JUNIPER, M. P. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171-195.
32. JUNIPER, M. P. 2007 The full impulse response of two-dimensional jet/wake flows and implications for confinement. J. Fluid Mech. 590, 163-185.
33. JUNIPER, M. P. & CANDEL, S. M. 2003 The stability of ducted compound flows and consequences for the geometry of coaxial injectors. J. Fluid Mech. 482, 257-269.
34. LEIBOVICH, S. 1983 Vortex stability and breakdown: Survey and extension. AIAA J. 22, 1192-1206.
35. LEIBOVICH, S. & KRIBUS, A. 1990 Large-amplitude wavetrains and solitary waves in vortices. J. Fluid Mech. 216, 459-504.
36. LIANG, H. & MAXWORTHY, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115-159.
37. LIM, D. W. & REDEKOPP, L. G. 1998 Absolute instability conditions for variable density, swirling jet flows. Eur. J. Mech. B Fluids 17, 165-185.
38. LOISELEUX, T., CHOMAZ, J.-M. & HUERRE, P. 1998 The effect of swirl on jets and wakes: Linear instability of the Rankine vortex with axial flow. Phys. Fluids 10, 1120-1134.
39. LOISELEUX, T., DELBENDE, I. & HUERRE, P. 2000 Absolute and convective instabilities of a swirling jet/wake shear layer. Phys. Fluids 12, 375-380.
40. LOPEZ, J. M. 1994 On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe. Phys. Fluids 6, 3683-3693.
41. MONKEWITZ, P. A. & SOHN, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911-916.
42. OLENDRARU, C., SELLIER, A., ROSSI, M. & HUERRE, P. 1999 Inviscid instability of the Batchelor vortex: Absolute-convective transition and spatial branches. Phys. Fluids 11, 1805-1820.
43. PIER, B., HUERRE, P. & CHOMAZ, J.-M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 49-96.
44. RUITH, M. R., CHEN, P., MEIBURG, E. & MAXWORTHY, T. 2003 Three-dimensional vortex breakdown in swirling jets and wakes: Direct numerical solution. J. Fluid Mech. 486, 331-378.
45. SARPKAYA, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545-559.
46. SPALL, R. E., GATSKI, T. B. & GROSCH, C. E. 1987 A criterion for vortex breakdown. Phys. Fluids 30, 3434-3440.
47. SQUIRE, H. B. 1956 Rotating fluids. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies), pp. 139-161. Cambridge University Press.
48. SQUIRE, H. B. 1960 Analysis of the vortex breakdown phenomenon. In Miszallaneen der Angewandten Mechanik, pp. 306-312. Berlin: Akademie.
49. TSAI, C.-Y. & WIDNALL, S. E. 1980 Examination of a group-velocity criterion for breakdown of vortex flow in a divergent duct. Phys. Fluids 23, 864-870.
50. WANG, S. & RUSAK, Z. 1996 On the stability of an axisymmetric rotating flow in a pipe. Phys. Fluids 8, 1007-1016.
51. WANG, S. & RUSAK, Z. 1997a The effect of slight viscosity on a near-critical swirling flow in a pipe. Phys. Fluids 9, 1914-1927.
52. WANG, S. & RUSAK, Z. 1997b The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown. J. Fluid Mech. 340, 177-223.
53. YU, M.-H. & MONKEWITZ, P. A. 1990 The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys. Fluids A 2, 1175-1181.