Direct Numerical Simulation and Implicit Large Eddy Simulation of Stratified Turbulence

  • S. Remmler
  • S. Hickel


Simulation of geophysical turbulent flows requires a robust and accurate subgrid-scale turbulence modeling. We propose an implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method. To validate this turbulence model, we performed direct numerical simulations of the transition of the three-dimensional Taylor–Green vortex and homogeneous stratified turbulence. Our analysis proves that the implicit turbulence model correctly predicts the turbulence energy budget and the spectral structure of stratified turbulence.


Large Eddy Simulation Direct Numerical Simulation Froude Number Inertial Range Direct Numerical Simulation Data 
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  1. 1.
    P. Bouruet-Aubertot, J. Sommeria, and C. Staquet. Stratified turbulence produced by internal wave breaking: Two-dimensional numerical experiments. Dyn. Atmos. Oceans, 23(1–4):357–369, 1996. Stratified flows. CrossRefGoogle Scholar
  2. 2.
    M. E. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf, and U. Frisch. Small-scale structure of the Taylor–Green vortex. J. Fluid Mech., 130:411–452, 1983. zbMATHCrossRefGoogle Scholar
  3. 3.
    M. E. Brachet. Direct simulation of three-dimensional turbulence in the Taylor–Green vortex. Fluid Dynam. Res., 8(1–4):1–8, 1991. CrossRefGoogle Scholar
  4. 4.
    G. Brethouwer, P. Billant, E. Lindborg, and J.-M. Chomaz. Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech., 585:343–368, 2007. zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    J.-P. Chollet and M. Lesieur. Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. Journal of the Atmospheric Sciences, 38(12):2747–2757, 1981. CrossRefGoogle Scholar
  6. 6.
    C. Cot. Equatorial mesoscale wind and temperature fluctuations in the lower atmosphere. J. Geophys. Res., 106(D2):1523–1532, 2001. CrossRefGoogle Scholar
  7. 7.
    E. M. Dewan. Stratospheric wave spectra resembling turbulence. Science, 204(4395):832–835, 1979. CrossRefGoogle Scholar
  8. 8.
    A. Dörnbrack. Turbulent mixing by breaking gravity waves. J. Fluid Mech., 375:113–141, 1998. zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    D. C. Fritts, L. Wang, J. Werne, T. Lund, and K. Wan. Gravity wave instability dynamics at high Reynolds numbers. Part I: Wave field evolution at large amplitudes and high frequencies. J. Atmos. Sci., 66(5):1126–1148, 2009. CrossRefGoogle Scholar
  10. 10.
    K. S. Gage. Evidence for a k −5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci., 36:1950–1954, October 1979. CrossRefGoogle Scholar
  11. 11.
    J. R. Herring and O. Métais. Numerical experiments in forced stably stratified turbulence. J. Fluid Mech., 202(1):97–115, 1989. CrossRefGoogle Scholar
  12. 12.
    S. Hickel, N. A. Adams, and J. A. Domaradzki. An adaptive local deconvolution method for implicit LES. J. Comput. Phys., 213:413–436, 2006. zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    S. Hickel, N. A. Adams, and N. N. Mansour. Implicit subgrid-scale modeling for large-eddy simulation of passive scalar mixing. Phys. Fluids, 19:095102, 2007. CrossRefGoogle Scholar
  14. 14.
    S. Hickel, T. Kempe, and N. A. Adams. Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions. Theor. Comput. Fluid Dyn., 22:227–242, 2008. zbMATHCrossRefGoogle Scholar
  15. 15.
    H.-J. Kaltenbach, T. Gerz, and U. Schumann. Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow. J. Fluid Mech., 280(1):1–40, 1994. zbMATHCrossRefGoogle Scholar
  16. 16.
    R. H. Kraichnan. Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10(7):1417–1423, 1967. CrossRefGoogle Scholar
  17. 17.
    J.-P. Laval, J. C. McWilliams, and B. Dubrulle. Forced stratified turbulence: Successive transitions with Reynolds number. Phys. Rev. E, 68(3):036308, September 2003. CrossRefGoogle Scholar
  18. 18.
    D. K. Lilly. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40(3):749–761, 1983. CrossRefGoogle Scholar
  19. 19.
    D. K. Lilly, G. Bassett, K. Droegemeier, and P. Bartello. Stratified turbulence in the atmospheric mesoscales. Theor. Comput. Fluid Dyn., 11:139–153, 1998. zbMATHCrossRefGoogle Scholar
  20. 20.
    E. Lindborg and G. Brethouwer. Stratified turbulence forced in rotational and divergent modes. J. Fluid Mech., 586:83–108, 2007. zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    E. Lindborg. The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550(1):207–242, 2006. zbMATHCrossRefGoogle Scholar
  22. 22.
    O. Métais and J. R. Herring. Numerical simulations of freely evolving turbulence in stably stratified fluids. J. Fluid Mech., 202(1):117–148, 1989. CrossRefGoogle Scholar
  23. 23.
    O. Métais and M. Lesieur. Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech., 239:157–194, 1992. zbMATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    G. D. Nastrom and K. S. Gage. A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42(9):950–960, 1985. CrossRefGoogle Scholar
  25. 25.
    J. J. Riley and S. M. de Bruyn Kops. Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids, 15(7):2047–2059, 2003. MathSciNetCrossRefGoogle Scholar
  26. 26.
    C.-W. Shu. Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput., 9(6):1073–1084, 1988. zbMATHCrossRefGoogle Scholar
  27. 27.
    L. M. Smith and F. Waleffe. Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech., 451(1):145–168, 2002. zbMATHGoogle Scholar
  28. 28.
    C. Staquet and F. S. Godeferd. Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics. J. Fluid Mech., 360:295–340, 1998. zbMATHMathSciNetCrossRefGoogle Scholar
  29. 29.
    H. A. van der Vorst. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 13(2):631–644, 1992. zbMATHCrossRefGoogle Scholar
  30. 30.
    T. E. van Zandt. A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9(5):575–578, 1982. CrossRefGoogle Scholar
  31. 31.
    M. L. Waite and P. Bartello. Stratified turbulence dominated by vortical motion. J. Fluid Mech., 517:281–308, 2004. zbMATHMathSciNetCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Aerodynamics and Fluid MechanicsTechnische Universität MünchenGarching bei MünchenGermany

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