Prototypical examples of stratified shear flow

  • Sutanu Sarkar
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 479)


Stratification effects on turbulence are examined in some fundamental shear flows. The differences between unbounded flows and those with walls are indicated. The role of the gradient Richardson number is assessed. Detailed results on turbulence energetics, transport and mixing are presented.


Shear Layer Turbulent Kinetic Energy Direct Numerical Simulation Richardson Number Horizontal Shear 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. V. Armenio and S. Sarkar. An investigation of stably stratified turbulent channel flow using large-eddy simulation. J. Fluid Mech., 459:1–42, 2002.MATHCrossRefADSGoogle Scholar
  2. V. Armenio and S. Sarkar. Mixing in a stably-stratified medium by horizontal shear near vertical walls. Theor. Comput. Fluid Dynamics, 17:331–349, 2004.MATHCrossRefADSGoogle Scholar
  3. S. P. S. Arya. Buoyancy effects in a horizontal flat-plate boundary layer. J. Fluid Mech., 68:321, 1975.CrossRefADSGoogle Scholar
  4. S. Basak and S. Sarkar. Dynamics of a Stratified Shear Layer with Horizontal Shear. submitted, 2005.Google Scholar
  5. J. H. Bell and R. D. Mehta. Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA J., 28:2034–2042, 1990.ADSCrossRefGoogle Scholar
  6. R. E. Britter. An experiment on turbulence in a density stratified fluid. PhD thesis, Monash Univerity, Australia, 1974.Google Scholar
  7. S. Scott Collis, Sanjiva K. Lele, Robert D. Moser, and Michael M. Rogers. The evolution of a plane mixing layer with spanwise nonuniform forcing. Phys. Fluids, 6(1):381–396, 1994.MATHCrossRefADSGoogle Scholar
  8. Pierre Comte, Marcel Lesieur, and Eric Lamballais. Large-scale and small-scale stirring of vorticity and a passive scalar in a 3-D temporal mixing layer. Phys. Fluids, 4(12): 2761–2778, 1992.CrossRefADSGoogle Scholar
  9. P. F. Crapper and P. F. Linden. The structure of turbulent density interfaces. J. Fluid Mech., 65:45, 1974.CrossRefADSGoogle Scholar
  10. P. E. Dimotakis and G. L. Brown. Mixing layer at high reynolds-number-large-structure dynamics and entrainment. J. Fluid Mech., 78:535, 1976.CrossRefADSGoogle Scholar
  11. D.M. Farmer, E.A. D’Asaro, M.V. Trevorrow, and G.T. Dairiki. Three-dimensional structure in a tidal convergence front. Continental Shelf Research, 15:1649–1673, 1995.CrossRefADSGoogle Scholar
  12. H. J. S. Fernando. Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech., 23:455–493, 1991.CrossRefADSGoogle Scholar
  13. P. Flament, R. Lumpkin, J. Tournadre, and L. Armi. Vortex pairing in an unstable anticyclonic shear flow: discrete subharmonics of one pendulum day. J. Fluid Mech., 440:401–409, 2001.MATHCrossRefADSGoogle Scholar
  14. K. S. Gage and W. H. Reid. The stability of thermally stratified plane Poiseuille flow. J. Fluid Mech., 33:21, 1968.MATHCrossRefADSGoogle Scholar
  15. R. P. Garg, J. H. Ferziger, S. G. Monismith, and J. R. Koseff. Stably stratified turbulent channel flows. I. Stratification regimes and turbulence suppression mechanism. Phys. Fluids, 12:2569, 2000.CrossRefADSGoogle Scholar
  16. T. Gerz, U. Schumann, and S. E. Elghobashi. Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech., 200:563–594, 1989.MATHCrossRefADSGoogle Scholar
  17. T. Gerz H.-J. Kaltenbach and U. Schumann. Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow. J. Fluid Mech., 280:1–40, 1994.MATHCrossRefADSGoogle Scholar
  18. M. A. Hernan and J. Jimenez. Computer-analysis of a high-speed film of the plane turbulent mixing layer. J. Fluid Mech., 119:323, 1982.CrossRefADSGoogle Scholar
  19. S. E. Holt, J. R. Koseff, and J. H. Ferziger. A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence. J. Fluid Mech., 237: 499–539, 1992.MATHCrossRefADSGoogle Scholar
  20. E. J. Hopfinger. Turbulence in stratified fluids: A review. J. Geophys. Res., 92:5287–5303, 1987.ADSCrossRefGoogle Scholar
  21. L. N. Howard. Note on a paper of John. W. Miles. J. Fluid Mech., 10:509–512, 1961.MATHCrossRefADSMathSciNetGoogle Scholar
  22. G. N. Ivey and J. Imberger. On the nature of turbulence in a stratified fluid. Part I: the energetics of mixing. J. Phys. Oceanogr., 21:650–658, 1991.CrossRefADSGoogle Scholar
  23. F. G. Jacobitz and S. Sarkar. The effect of nonvertical shear on turbulence in a stably stratified medium. Phys. Fluids, 10(5):1158–1168, 1998.CrossRefADSMathSciNetMATHGoogle Scholar
  24. F. G. Jacobitz and S. Sarkar. On the Shear Number Effect in Stratified Shear Flow. Theor. Comput. Fluid Dynamics, 13:171–188, 1999a.MATHCrossRefADSGoogle Scholar
  25. F. G. Jacobitz and S. Sarkar. A direct numerical study of transport and anisotropy in a stably stratified turbulent flow with uniform horizontal shear. Flow, Turbulence and Combustion., 63:343–360, 1999b.CrossRefGoogle Scholar
  26. F. G. Jacobitz, S. Sarkar, and C. W. VanAtta. Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow. J. Fluid Mech., 342:231–261, 1997.MATHCrossRefADSGoogle Scholar
  27. J.A. Johannessen, R.A. Schuman, G. Digranes, D.R. Lyzenga, C. Wackerman, O.M. Johannessen, and P. W. Vachon. Coastal ocean fronts and eddies imaged with ERS 1 synthetic aperture radar. J. Geophys. Res., 101:6651–6667, 1996.CrossRefADSGoogle Scholar
  28. S. Komori. Turbulence structure in stratified flow. PhD thesis, Kyoto Univerity, Japan, 1980.Google Scholar
  29. S. Komori, H. Ueda, F. Ogino, and T. Mizushina. Turbulence structures in stably stratified open-channel flow. J. Fluid Mech., 130:13–26, 1983.CrossRefADSGoogle Scholar
  30. B. Kosovic and J. A. Curry. A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57:1052, 2000.CrossRefADSMathSciNetGoogle Scholar
  31. M. Lesieur. Turbulence in fluids, 3rd edn. Springer, 1997.Google Scholar
  32. R. Lien and T.B. Sanford. Turbulence spectra and local similarity scaling in a strongly stratified oceanic bottom boundary layer. Continental Shelf Research, 24:375–392, 2004.CrossRefADSGoogle Scholar
  33. J. T. Lin and Y. H. Pao. Wakes in stratified fluids. Ann. Rev. Fluid Mech., 11:317–338, 1979.CrossRefADSGoogle Scholar
  34. Y. Lu, R. G. Lueck, and D. Huang. The effect of stable thermal stratification on the stability of viscous parallel flows. J. Phys. Oceanogr., 30:855–867, 2000.CrossRefADSGoogle Scholar
  35. L. Mahrt. Stratified atmospheric boundary layers. Boundary-Layer Meteorology, 90: 375–396, 1999.CrossRefADSGoogle Scholar
  36. P. J. Mason and S. H. Derbyshire. Large eddy simulation of the stably-stratified atmospheric boundary layer. Boundary-Layer Met., 53:117, 1990.CrossRefADSGoogle Scholar
  37. J. W. Miles. On the stability of heterogeneous shear flows. J. Fluid Mech., 10:496–508, 1961.MATHCrossRefADSMathSciNetGoogle Scholar
  38. M. J. Moore and R. R. Long. An experimental investigation of turbulent stratified shearing flow. J. Fluid Mech., 49:635–655, 1971.CrossRefADSGoogle Scholar
  39. P. Müller, G. Holloway, F. Henyey, and N. Pomphrey. Nonlinear interactions among gravity waves. Rev. Geophys., 24:493–536, 1986.ADSCrossRefGoogle Scholar
  40. W. Munk, L. Armi, K. Fischer, and F. Zachariasen. Spirals on the sea. Proc. R. Soc. Lond. A, 456:1217–1280, 2000.MATHADSMathSciNetCrossRefGoogle Scholar
  41. R. Nagaosa and T. Saito. Turbulence structure and scalar transfer in stably stratified free-surface flows. AIChE J., 43:2393, 1997.CrossRefGoogle Scholar
  42. K. J. Nygaard and A. Glezer. The effect of phase variations and cross-shear on vortical structures in a plane mixing layer. J. Fluid Mech., 276:21–59, 1994.CrossRefADSGoogle Scholar
  43. Y. Pan and S. Banerjee. A numerical study of free-surface turbulence in channel flow. Phys. Fluids, 7:1649–1664, 1995.MATHCrossRefADSGoogle Scholar
  44. W. R. Peltier and C. P. Caulfield. Mixing efficiency in stratified shear flows. Ann. Rev. Fluid Mech., 35:135–167, 2003.CrossRefADSMathSciNetGoogle Scholar
  45. J. F. Piat and E. J. Hopfinger. A boundary layer topped by a density interface. J. Fluid Mech., 113:411, 1981.CrossRefADSGoogle Scholar
  46. P. S. Piccirillo and C. W. VanAtta. The evolution of a uniformly sheared thermally stratified turbulent flow. J. Fluid Mech., 334:61–86, 1997.CrossRefADSGoogle Scholar
  47. J. J. Riley and M. P. Lelong. Fluid motions in the presence of strong stable stratification. Ann. Rev. Fluid Mech., 32:613–657, 2000.CrossRefADSMathSciNetGoogle Scholar
  48. R. S. Rogallo. Numerical experiments in homogeneous turbulence. NASA TM 81315, 1981.Google Scholar
  49. M. M. Rogers, P. Moin, and W. C. Reynolds. The structure and modeling of the hydrodynamic and passive scalar fields in homogeneous turbulent shear flow. PhD thesis, Stanford University, Report TF-25, Mechanical Engr., 1989.Google Scholar
  50. M. M. Rogers and R. D. Moser. Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids, 6(2):903–923, 1994.MATHCrossRefADSGoogle Scholar
  51. J. J. Rohr, E. C. Itsweire, K. N. Helland, and C. W. VanAtta. Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech., 195:77–111, 1988.MATHCrossRefADSMathSciNetGoogle Scholar
  52. E. S. Saiki, C. H. Moeng, and P. P. Sullivan. Large-eddy simulation of the stably-stratified planetary boundary layer. Boundary-Layer Met., 53:117, 1990.CrossRefGoogle Scholar
  53. U. Schumann and T. Gerz. Turbulent mixing in stably stratified shear flows. J. Appl. Meteor., 34:33, 1995.ADSCrossRefGoogle Scholar
  54. L. H. Shih, J. R. Koseff, J. H. Ferziger, and C. R. Rehmann. Scaling and parameterization of stratified homogeneous turbulent shear flow. J. Fluid Mech., 412:1–20, 2000.MATHCrossRefADSGoogle Scholar
  55. M. T. Stacey, S. G. Monismith, and J. R. Barua. Observations of turbulence in a partially stratified estuary. J. Phys. Oceanogr., 29:1950–1970, 1999.CrossRefADSGoogle Scholar
  56. S. Tavoularis and U. Karnik. Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence. J. Fluid Mech., 204:457–478, 1989.CrossRefADSGoogle Scholar
  57. J. Taylor, S. Sarkar, and V. Armenio. Large eddy simulation of stably stratified open channel flow, submitted, 2005.Google Scholar
  58. K. B. Winters and E. A. DAsaro. Diascalar flux and the rate of fluid mixing. J. Fluid Mech., 317:179–193, 1996.MATHCrossRefADSGoogle Scholar
  59. K. B. Winters, P. N. Lombard, J. J. Riley., and E. A. DAsaro. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech., 289:115–128, 1995.MATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Sutanu Sarkar
    • 1
  1. 1.University of California at San DiegoSan Diego

Personalised recommendations