Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-07T13:46:21.602Z Has data issue: false hasContentIssue false
  • English
  • Français

Instability of strained vortex layers and vortex tube formation in homogeneous turbulence

Published online by Cambridge University Press:  26 April 2006

T. Passot ,
H. Politano ,
P.L. Sulem ,
J.R. Angilella  and
M. Meneguzzi
T. Passot
Affiliation:
CNRS URA 1362, Observatoire de la Côte d'Azur, BP 229, 06304 Nice Cedex 4, France
H. Politano
Affiliation:
CNRS URA 1362, Observatoire de la Côte d'Azur, BP 229, 06304 Nice Cedex 4, France
P.L. Sulem
Affiliation:
CNRS URA 1362, Observatoire de la Côte d'Azur, BP 229, 06304 Nice Cedex 4, France
J.R. Angilella
Affiliation:
CERFACS, 42 Avenue G. Coriolis, 31057 Toulouse, France
M. Meneguzzi
Affiliation:
CERCA, 5160 Boulevard Décarie, Montreal, Quebec H2X 2H9, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

A modulational perturbation analysis is presented which shows that when a strained vortex layer becomes unstable, vorticity concentrates into steady tubular structures with finite amplitude, in quantitative agreement with the numerical simulations of Lin & Corcos (1984). Elaborated three-dimensional visualizations suggest that this process, due to a combination of compression and self-induced rotation of the layer, is at the origin of intense and long-lived vortex tubes observed in direct numerical simulations of homogeneous turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 313 - 338
Copyright
© 1995 Cambridge University Press

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

Angilella, J. R., Astruc, D. & Vincent, A. 1993 The cone of vision: a new technique for an interactive volumetric display. ACM Transaction on Graphics (submitted).
Ashurst, W.T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30. 2343–2353.Google Scholar
Baker, G. R. & Shelley, M.J. 1990 On the connection between thin vortex layers and vortex sheets. J. Fluid Mech. 215. 161–194.Google Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1. 497–504.Google Scholar
Bonn, D., Couder, Y., Dam, P.H.J. Van & Douady, S. 1993 From small scales to large scales in three-dimensional turbulence: The effect of diluted polymers. Phys. Rev. E 47. R28–R31.Google Scholar
Brachet, M. E. 1991 Direct simulation of three-dimensional turbulence in the Taylor-Green vortex. Fluid Dyn. Res. 8. 1–8.Google Scholar
Brachet, M. E., Meneguzzi, M., Vincent, A., Politano, H. & Sulem, P. L. 1992 Numerical existence of smooth self-similar dynamics and possibility of subsequent collapse for three-dimensional ideal flows. Phys. Fluids A 4. 2845–2854.Google Scholar
Cadot, O., Douady, S. & Couder, Y. 1994 Characterisation of the low pressure filaments in a 3D turbulent shear flow. Phys. Fluids (to appear).Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vorticity filaments In Phys. Rev. Lett. 67. 982–986.Google Scholar
Gagne, Y. & Castaing, B. 1991 Une représentation universelle sans invariance globale d‘echelle des spectres d'energie en turbulence développée. C.R. Acad. Sci. Paris 312. 441–445.Google Scholar
Herring, J. R. & Kerr, R. M. 1993 Development of enstrophy and spectra in numerical turbulence. Phys. Fluids A 5. 2792–2798.Google Scholar
Jiménez, J. 1992 Kinematic alignment effects in turbulent flows. Phys. Fluids A 4. 652–654.Google Scholar
Jiménez, J. & Wray, A. A. 1994 Intense vortices in isotropic turbulence. Proc. Fifth European Turbulence Conference, Siena, July 1994, to appear.
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255. 65–90.Google Scholar
Kerr, R. M. 1985 Higher-order derivative conclusions and the alignment of small-scale structures in isotrophic numerical turbulence. J. Fluid Mech. 153. 31–58.Google Scholar
Kida, S. & Ohkitani, K. 1992 Spatio-temporal intermittency and instability of a forced turbulence. Phys. Fluids A 4. 1018–1027.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141. 139–178.Google Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25. 2193–2203.Google Scholar
Lundgren, T.S. 1993 A small scale turbulent model. Phys. Fluids A 5. 1472–1483.Google Scholar
Majda, A. 1986 Vorticity and the mathematical theory of incompressible fluid flow. Commun. Pure Appl. Maths 39. S187–S220.Google Scholar
Meiron, D. I., Baker, G. R. & Orszag, S. A. 1982 Analytic structure of vortex sheet dynamics. Part 1. Kelvin-Helmoltz instability. J. Fluid Mech. 114. 283–298.Google Scholar
Moffatt, H. K., Kida, S. & Ohkitani, K. 1994 Stretched vortices - the sinews of turbulence; large Reynolds number asymptotics. J. Fluid Mech. 259. 241–264.Google Scholar
Neu, J.C. 1984 The dynamics of stretched vortices. J. Fluid Mech. 143. 253–276.Google Scholar
Novikov, E. A. 1993 Statistical balance of vorticity and a new scale for vortical structures in turbulence. Phys. Rev. Lett. 71. 2718–2720.Google Scholar
Palais, B. 1988 Blowup for nonlinear equations using a comparison principle in Fourier space. Commun. Pure Appl. Maths 41. 165–196.Google Scholar
Porter, D.H., Pouquet, A. & Woodward, R. P. 1992 Three-dimensional supersonic homogeneous turbulence: a numerical study. Phys. Rev. Lett. 68. 3156–3159.Google Scholar
Porter, D. H., Pouquet, A. & Woodward, R. P. 1994 Kolmogorov-like spectra in decaying three-dimensional supersonic turbulence. Phys. Fluids 6. 2133–2142.Google Scholar
Pumir, A. 1994 A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, isotropic turbulence. Phys. Fluids 6. 2071–2083.Google Scholar
Ruetsch, G. R. & Maxey, M. R. 1991 Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids A 3. 1587–1597.Google Scholar
Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4. 2747–2760.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
She, Z. S. & Jackson, E. 1993 On the universal form of energy spectra in fully developed turbulence. Phys. Fluids A 5. 1526–1528.Google Scholar
She, Z. S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344. 226–228.Google Scholar
She, Z.S., Jackson, E. & Orszag, S. A. 1991 Structure and dynamics of homogeneous turbulence: Models and simulations. Proc R. Soc. Lond. A 434. 101–124.Google Scholar
Siggia, E.D. 1981 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107. 375–406.Google Scholar
Sulem, C., Sulem, P. L. & Frisch, H. 1983 Tracing complex singularities with spectral methods. J. Comput. Phys. 50. 138–161.Google Scholar
Tanaka, M. & Kida, S. 1993 Characterisation of vortex tubes and sheets. Phys. Fluids A 5. 2079–2082.Google Scholar
Townsend, A. A. 1951 On the fine scale structure of turbulence. Proc. R. Soc. Lond. A 208. 534–542.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225. 1–20.Google Scholar
Vincent, A. & Meneguzzi, M. 1994 On the dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258. 245–254.Google Scholar