Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-11T10:39:04.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute instability in axisymmetric wakes: compressible and density variation effects

Published online by Cambridge University Press:  26 March 2008

PHILIPPE MELIGA ,
DENIS SIPP  and
JEAN-MARC CHOMAZ
PHILIPPE MELIGA
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
DENIS SIPP
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
JEAN-MARC CHOMAZ
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France LadHyX, CNRS-Ecole Polytechnique, 91128 Palaiseau, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Lesshafft & Huerre (Phys. Fluids, 2007; vol. 19, 024102) have recently studied the transition from convective to absolute instability in hot round jets, for which absolute instability is led by axisymmetric perturbations and enhanced when lowering the jet density. The present paper analyses similarly the counterpart problem of wake flows, and establishes that absolute instability is then led by a large-scale helical wake mode favoured when the wake is denser than the surrounding fluid. This generalizes to variable density and compressible wakes the results of Monkewitz (J. Fluid Mech. vol 192, 1988, p. 561). Furthermore, we show that in a particular range of density ratios, the large-scale helical wake mode can become absolutely unstable by increasing only the Mach number up to high subsonic values. This possibility of an absolute instability triggered by an increase of the Mach number is opposite to the behaviour previously described in shear flows such as plane mixing layers and axisymmetric jets. A physical interpretation based on the action of the baroclinic torque is proposed. An axisymmetric short-scale mode, similar to that observed in plane mixing layers, leads the transition in light wakes, but the corresponding configurations require large counterflow for the instability to be absolute.

These results suggest that the low-frequency oscillation present in afterbody wakes may be due to a nonlinear global mode triggered by a local absolute instability, since the azimuthal wavenumber and absolute frequency of the helical wake mode agree qualitatively with observations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 373 - 401
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209–221.CrossRefGoogle Scholar
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.CrossRefGoogle Scholar
Berger, E., Scholz, D. & Schumm, M. 1990 Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations. J. Fluids Struct. 4, 231–257.CrossRefGoogle Scholar
Bers, A. 1975 Linear waves and instabilities. In Plasma Physics (by Witt, C. De, & Peyraud, J. ed.), 117–215. Gordon & Breach.Google Scholar
Boyd, J. P. 1989 Chebyshev and Fourier Spectral Methods. Springer.CrossRefGoogle Scholar
Briggs, R. J. 1964 Electron Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Carroll, L. 1872 Through the Looking-Glass: and What Alice Found There. MacMillan.Google Scholar
Chomaz, J. M. 1992 Absolute and convective instability in non linear systems. Phys. Rev. Lett. 69, 1931–1934.CrossRefGoogle Scholar
Chomaz, J. M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid. Mech. 37, 357–392.CrossRefGoogle Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 25–28.CrossRefGoogle ScholarPubMed
Couairon, A. & Chomaz, J.-M. 1997 Absolute and convective instabilities, front velocities and global modes in nonlinear systems. Physica D 108, 236–276.Google Scholar
Couairon, A. & Chomaz, J.-M. 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11 (12), 3688–3703.CrossRefGoogle Scholar
Dee, G. & Langer, J. 1983 Propagating pattern selection. Phys. Rev. Lett. 50, 383–386.CrossRefGoogle Scholar
Deissler, R. J. 1987 The convective nature of instability in plane Poiseuille flow. Phys. Fluids 30 (8), 2303–2305.CrossRefGoogle Scholar
Depres, D., Reijasse, P. & Dussauge, J. P. 2004 Analysis of unsteadiness in afterbody transonic flows. AIAA J. 42, 2541–2550.CrossRefGoogle Scholar
Drazin, P. & Reid, W. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Flodrops, J. P. & Desse, J. M. 1985 Sillage d'un culot axisymétrique. Rapport 85/19. Institut de Mécanique des Fluides de Lille, France.Google Scholar
Fuchs, H. V., Mercker, E. & Michel, U. 1979 Large-scale coherent structures in the wake of axisymmetric bodies. J. Fluid Mech. 93, 185–207.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J. M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223–253.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Hammond, D. & Redekopp, L. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231–260.CrossRefGoogle Scholar
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.Google ScholarPubMed
Healey, J. J. 2006 A new convective instability of the rotating-disk boundary layer with growth normal to the disk. J. Fluid Mech. 560, 279–310.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilies in free shear layers. J. Fluid Mech. 159, 151–168.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities (Godrèche, C. & Manneville, P. ed.) 81–294. Cambridge University Press.CrossRefGoogle Scholar
Jendoubi, S. & Strykowski, P. J. 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6 (9), 3000–3009.CrossRefGoogle Scholar
Juniper, M. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171–195.CrossRefGoogle Scholar
Kim, H. J. & Durbin, P. A. 1988 Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 31 (11), 3260–3265.CrossRefGoogle Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.CrossRefGoogle Scholar
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19 (2), 024102.CrossRefGoogle Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393–409.CrossRefGoogle Scholar
Miles, J. W. 1958 On the disturbed motion of a plane vortex sheet. J. Fluid Mech. 4, 538–552.CrossRefGoogle Scholar
Monkewitz, P. A. 1988 A note on vortex shedding from axisymmetric bluff bodies. J. Fluid Mech. 192, 561–575.CrossRefGoogle Scholar
Monkewitz, P. A. & Nguyen, L. N. 1987 Absolute instability in the near-wake of two-dimensional bluff-bodies. J. Fluids Struct. 1, 165–184.CrossRefGoogle Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.CrossRefGoogle Scholar
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.CrossRefGoogle Scholar
Nichols, J. W., Schmid, P. J. & Riley, J. J. 2007 Self-sustained oscillations in variable-density round jets. J. Fluid Mech. 582, 341–376.CrossRefGoogle Scholar
Pavithran, S. & Redekopp, L. G. 1989 The absolute-convective transition in subsonic mixing layers. Phys. Fluids A 1 (10), 1736–1739.CrossRefGoogle Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407–417.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145–174.CrossRefGoogle Scholar
Pier, B., Huerre, P. & Chomaz, J. M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 49–96.Google Scholar
van Saarloos, W. 1987 Dynamical velocity selection: marginal stability. Phys. Rev. Lett. 58, 2571–2574.CrossRefGoogle Scholar
van Saarloos, W. 2003 Front propagation into unstable states. Phys. Rep. 386, 29–222.CrossRefGoogle Scholar
Sato, H. & Okada, O. 1966 The stability and transition of an axisymmetric wake. J. Fluid Mech. 26, 237–253.CrossRefGoogle Scholar
Schlichting, H. 1978 Boundary-Layer Theory, 7th edn. McGraw–Hill.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Sevilla, A. & Martínez-Bazàn, C. 2004 Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: local linear instability and global bleed control. Phys. Fluids 16 (9), 3460–3469.CrossRefGoogle Scholar
Soteriou, M. C. & Ghoniem, A. F. 1995 Effects of the free-stream density ratio on free and forced spatially developing shear layers. Phys. Fluids 7 (8), 2036–2051.CrossRefGoogle Scholar
Tobias, S. M., Proctor, M. R. E. & Knobloch, E. 1997 The role of absolute instability in the solar dynamo. Astron. Astrophys. 318, 55–58.Google Scholar
Tobias, S. M., Proctor, M. R. E. & Knobloch, E. 1998 Convective and absolute instabilities of fluid flows in finite geometry. Physica D 113, 4–72.Google Scholar
Yu, M. H. & Monkewitz, P. A. 1990 The effect of non uniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys. Fluids A 2 (7), 1175–1181.CrossRefGoogle Scholar