Skip to main content

A Numerical Study of Turbulent Stably-Stratified Plane Couette Flow

  • Conference paper
High Performance Computing in Science and Engineering '10

Abstract

Direct numerical simulations (DNS) of stably-stratified, turbulent plane Couette flow are currently being performed on the XC-4000. The friction Reynolds number is kept approximately constant, Re τ ≃540 and the Richardson number Ri w varies between 0 and 0.1. The flow is divided into two regions: the region close to the wall and the core region. The region close to the wall presents strong velocity and density gradients and its structure is similar to unstratified wall-turbulence. In the core region, the gradients of mean velocity and density are approximately constant, and the structure of the flow is similar to homogeneous stratified turbulence with shear. With increasing stratification the formation of layers is clearly observed. The layers are inclined with respect to the wall plane and their thickness decreases with increasing stratification.

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 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover 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. J.S. Turner. Buoyancy effects in fluids. Cambridge Univ. Press, 1973.

    Google Scholar 

  2. F.T.M. Nieuwstadt. The turbulent structure of the stable, nocturnal boundary layer. Journal of the Atmospheric Sciences, 41(14):2202–2216, 1984.

    Article  Google Scholar 

  3. R.B. Stull. An introduction to boundary layer meteorology. Kluwer Academic, 1999.

    Google Scholar 

  4. S.A. Thorpe. The turbulent ocean. Cambridge Univ. Press, Cambridge 2005.

    Google Scholar 

  5. C. Wunsch and R. Ferrari. Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36:281–314, 2004.

    Article  MathSciNet  Google Scholar 

  6. G.N. Ivey, K.B. Winters, and J.R. Koseff. Density stratification, turbulence, but how much mixing? Annu. Rev. Fluid Mech., 40:169–184, 2008.

    Article  MathSciNet  Google Scholar 

  7. G. Brethouwer, P. Billant, and E. Lindborg. Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech., 585:343–368, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  8. J.J. Riley and E. Lindborg. Stratified turbulence: a possible interpretation of some geophysical turbulence measurements. J. Atmos. Sci., 65:2416–2424, 2008.

    Article  Google Scholar 

  9. M. García-Villalba and J.C. del Álamo. Turbulence and internal waves in a stably-stratified channel flow. In W.E. Nagel et al., editor, High Performance Computing in Science and Engineering ’08, pages 217–227. Springer, 2008.

    Google Scholar 

  10. M. García-Villalba and J.C. del Álamo. Turbulence modification by stable stratification in channel flow. In preparation, 2010.

    Google Scholar 

  11. S. Komori, H. Ueda, F. Ogino, and T. Mizushina. Turbulent structure in stably stratified open-channel flow. J. Fluid Mech., 130:13–26, 1983.

    Article  Google Scholar 

  12. V. Armenio and S. Sarkar. An investigation of stably stratified turbulent channel flow using large-eddy simulation. J. Fluid Mech., 459:1–42, 2002.

    Article  MATH  Google Scholar 

  13. A. Lundbladh and A.V. Johansson. Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech., 229:499–516, 1991.

    Article  MATH  Google Scholar 

  14. K.H. Bech, N. Tillmark, P.H. Alfredsson, and H.I. Andersson. An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech., 286:291–325, 1995.

    Article  Google Scholar 

  15. J. Komminaho, A. Lundbladh, and A.V. Johansson. Very large structures in plane turbulent Couette flow. J. Fluid Mech., 320:259–285, 1996.

    Article  MATH  Google Scholar 

  16. C.H. Liu. Turbulent plane Couette flow and scalar transport at low Reynolds numbers. J. Fluid Mech., 286:291–325, 1995.

    Article  Google Scholar 

  17. T. Tsukahara, H. Kawamura, and K. Shingai. DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbulence, 7(19), 2006.

    Google Scholar 

  18. C.P. Caulfield and R.R. Kerswell. Maximal mixing rate in turbulent stably stratified Couette flow. Phys. Fluids, 13(4):894–900, 2001.

    Article  MathSciNet  Google Scholar 

  19. C.P. Caulfield, W. Tang, and S.C. Plasting. Reynolds number dependence of an upper bound for the long-time-averaged buoyancy flux in plane stratified Couette flow. J. Fluid Mech., 498:315–332, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  20. W. Tang, C.P. Caulfield, and R.R. Kerswell. A prediction for the optimal stratification for turbulent mixing. J. Fluid Mech., 634:487–497, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. Kim, P. Moin, and R. Moser. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech., 177:133–166, 1987.

    Article  MATH  Google Scholar 

  22. P.R. Spalart, R.D. Moser, and M.M. Rogers. Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions. J. Comp. Phys., 96:297–324, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  23. J.C. del Álamo and J. Jiménez. Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids, 15:L41–L44, 2003.

    Article  Google Scholar 

  24. J.C. del Álamo, J. Jiménez, P. Zandonade, and R.D. Moser. Scaling of the energy spectra in turbulent channels. J. Fluid Mech., 500:135–144, 2004.

    Article  MATH  Google Scholar 

  25. E. Azagra. Mixing efficiency in stably-stratified turbulent Couette flow. Master thesis, Karlsruhe Institute of Technology, 2009.

    Google Scholar 

  26. J. Miles. On the stability of heterogeneous shear flows. J. Fluid Mech., 10:496–508, 1961.

    Article  MATH  MathSciNet  Google Scholar 

  27. P.F. Linden. Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn., 13:3–23, 1979.

    Article  Google Scholar 

  28. W.D. Smyth and J.N. Moum. Length scales of turbulence in stably stratified mixing layers. Phys. Fluids, 12(6):1327–1342, 2000.

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manuel García-Villalba .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

García-Villalba, M., Azagra, E., Uhlmann, M. (2011). A Numerical Study of Turbulent Stably-Stratified Plane Couette Flow. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering '10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15748-6_19

Download citation

Publish with us

Policies and ethics