Skip to main content

Direct Numerical Simulation and Implicit Large Eddy Simulation of Stratified Turbulence

  • Conference paper
High Performance Computing in Science and Engineering '11
  • 1980 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  3. M. E. Brachet. Direct simulation of three-dimensional turbulence in the Taylor–Green vortex. Fluid Dynam. Res., 8(1–4):1–8, 1991.

    Article  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  6. C. Cot. Equatorial mesoscale wind and temperature fluctuations in the lower atmosphere. J. Geophys. Res., 106(D2):1523–1532, 2001.

    Article  Google Scholar 

  7. E. M. Dewan. Stratospheric wave spectra resembling turbulence. Science, 204(4395):832–835, 1979.

    Article  Google Scholar 

  8. A. Dörnbrack. Turbulent mixing by breaking gravity waves. J. Fluid Mech., 375:113–141, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  11. J. R. Herring and O. Métais. Numerical experiments in forced stably stratified turbulence. J. Fluid Mech., 202(1):97–115, 1989.

    Article  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  16. R. H. Kraichnan. Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10(7):1417–1423, 1967.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  18. D. K. Lilly. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40(3):749–761, 1983.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  20. E. Lindborg and G. Brethouwer. Stratified turbulence forced in rotational and divergent modes. J. Fluid Mech., 586:83–108, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  21. E. Lindborg. The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550(1):207–242, 2006.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  23. O. Métais and M. Lesieur. Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech., 239:157–194, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  25. J. J. Riley and S. M. de Bruyn Kops. Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids, 15(7):2047–2059, 2003.

    Article  MathSciNet  Google Scholar 

  26. C.-W. Shu. Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput., 9(6):1073–1084, 1988.

    Article  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  30. T. E. van Zandt. A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9(5):575–578, 1982.

    Article  Google Scholar 

  31. M. L. Waite and P. Bartello. Stratified turbulence dominated by vortical motion. J. Fluid Mech., 517:281–308, 2004.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Remmler .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Remmler, S., Hickel, S. (2012). Direct Numerical Simulation and Implicit Large Eddy Simulation of Stratified Turbulence. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23869-7_38

Download citation

Publish with us

Policies and ethics