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Spiral small-scale structures in compressible turbulent flows

  • Thomas Gomez
  • Hélène Politano
  • Annick Pouquet
  • Michèle LarchevÊque
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)

Abstract

We extend the spiral vortex solution of Lundgren 1982 to compressible turbulent flows following a perfect gas law. Lundgren’s model links the dynamical and spectral properties of incompressible flows, providing a k −5/3 Kolmogorov spectrum. A similar compressible spatio-temporal transformation is now derived, reducing the dynamics of three-dimensional (3D) vortices stretched by an axisymmetric incompressible strain into a 2D compressible vortex dynamics. It enables to write the 3D spectra of the incompressible and compressible square velocities u s 2 and u d 2 in terms of, respectively, the 2D spectra of the enstrophy and of the square velocity divergence, by use of a temporal integration (Gomez &al. 2001). New numerical results are presented now using 10242 gridpoints; initially, the r.m.s. Mach number is 0.32, with local values up to 0.9, the Reynolds number is 1,400, and x=u s 2 /u d 2 =0.1. A k −5/3 inertial behaviour is seen to result from the dynamical evolution for both the compressible and incompressible three-dimensional kinetic energy spectra.

Keywords

Mach Number Velocity Divergence Temporal Integration Compressible Structure Spiral Vortex 
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References

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Thomas Gomez
    • 1
  • Hélène Politano
    • 2
  • Annick Pouquet
    • 3
  • Michèle LarchevÊque
    • 1
  1. 1.LMM, Université Pierre & Marie CurieParisFrance
  2. 2.Observatoire de la Côte d’Azur, NiceNiceFrance
  3. 3.ASP/NCARBoulderUSA

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