The Relevance of a Back-Scatter Model for Depth-Averaged Flow Simulation

  • Bram C. van Prooijen
  • Wim S. J. UijttewaalEmail author
Open Access


This study demonstrates the importance of a sophisticated sub-grid model when performing a depth-averaged unsteady RANS simulation of a shallow flow. The reduction of resolution and the spatial dimensions exclude important physical processes as present in three-dimensional turbulence. Especially the effect of the bottom turbulence on the formation of horizontal eddies appears of key importance. A method is proposed to incorporate these effects by means of a kinematic simulation that mimics the residual turbulent fluctuations in a straight channel flow after depth-averaging. This method is developed in the context of the evolution of large eddies in a shallow mixing layer. A comparison with experiments shows that the proposed method works satisfactory. Naturally, it does not fully account for the omission of all 3D-effects.


Open channel Large eddy simulation Shallow flow Mixing layer 


  1. 1.
    Balaras, E., Benocci, C., Piomelli, U.: Two-layer approximate boundary conditions for large-eddy simulation. AIAA. J. 34(6), 1111–1119 (1996)zbMATHCrossRefADSGoogle Scholar
  2. 2.
    Batchelor, G.K.: Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl. II, 233–239 (1969)ADSGoogle Scholar
  3. 3.
    Brown, G.L., Roshko, A.: On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816 (1974). doi:10.1017/S002211207400190X CrossRefADSGoogle Scholar
  4. 4.
    Carati, D., Ghosal, S., Moin, P.: On the representation of backscatter in dynamic localization models. Phys. Fluids 7(3), 606–616 (1995). doi:10.1063/1.868585 zbMATHCrossRefADSGoogle Scholar
  5. 5.
    Chu, V.H., Babarutsi, S.: Confinement and bed-friction effects in shallow turbulent mixing layers. J. Hydraul. Eng. 114, 1257–1274 (1988)CrossRefGoogle Scholar
  6. 6.
    Domaradski, J.A., Saiki, E.M.: A subgrid-scale model based on the estimation of unresolved scales of turbulence. Phys. Fluids 9(7), 2148–2164 (1997). doi:10.1063/1.869334 CrossRefADSGoogle Scholar
  7. 7.
    Dracos, T., Giger, M., Jirka, G.H.: Plane turbulent jets in a bounded fluid layer. J. Fluid Mech. 214, 587–614 (1992). doi:10.1017/S0022112092002167 CrossRefADSGoogle Scholar
  8. 8.
    Elder, J.W.: The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5, 544–560 (1959)zbMATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H.: Mixing in Inland and Coastal Waters. Academic, New York (1979)Google Scholar
  10. 10.
    Flohr, P., Vassilicos, J.C.: A scalar subgrid model with flow structure for large-eddy simulations of scalar variances. J. Fluid Mech. 407, 315–349 (2000). doi:10.1017/S0022112099007533 zbMATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Fung, J.C.F., Hunt, J.C.R., Malik, N.A., Perkins, R.J.: Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J. Fluid Mech. 236, 281–318 (1992). doi:10.1017/S0022112092001423 zbMATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Hamba, F.: A Hybrid RANS/LES simulation of turbulent channel flow. Theor. Comput. Fluid Dyn. 16, 387–403 (2003). doi:10.1007/s00162-003-0089-x zbMATHCrossRefGoogle Scholar
  13. 13.
    Hinterberger, C.: Three-dimensional and depth averaged large eddy simulation of shallow water flows. PhD-thesis University of Karlsruhe, Germany (in German) (2004)Google Scholar
  14. 14.
    Hinterberger, C., Fröhlich, J., Rodi, W.: Three-dimensional and depth-averaged large-eddy simulations of some shallow water flows. J. Hydraul. Eng. 133(8), 857–872 (2007). doi:10.1061/(ASCE)0733-9429(2007)133:8(857) CrossRefGoogle Scholar
  15. 15.
    Hinterberger, C., Fröhlich, J., Rodi, W.: 2D and 3D turbulent fluctuations in open channel flow with Reτ = 590 studied by large eddy simulation. Flow Turbul. Combust. 80, 225–253 (2008). doi:10.1007/s10494-007-9122-2 CrossRefGoogle Scholar
  16. 16.
    Jiménez, J.: The physics of wall turbulence. Physica A 263, 252–262 (1999). doi:10.1016/S0378-4371(98)00507-X CrossRefADSGoogle Scholar
  17. 17.
    Johansson, P.S., Andersson, H.I.: Generation of inflow data for inhomogeneous turbulence. Theor. Comput. Fluid Dyn. 18, 371–389 (2004). doi:10.1007/s00162-004-0147-z zbMATHCrossRefGoogle Scholar
  18. 18.
    Kim, K.C., Adrian, R.J.: Very large-scale motion in the outer layer. Phys. Fluids 11(2), 417–422 (1999). doi:10.1063/1.869889 zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Li, N., Balaras, E., Piomelli, U.: Inflow conditions for large-eddy simulations of mixing layers. Phys. Fluids 12(4), 935–938 (2000)zbMATHCrossRefADSGoogle Scholar
  20. 20.
    Mason, P.J., Thomson, D.J.: Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid. Mech. 242, 51–78 (1992). doi:10.1017/S0022112092002271 zbMATHCrossRefADSGoogle Scholar
  21. 21.
    Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Reτ = 590. Phys. Fluids. 11(4), 943–945 (1999). doi:10.1063/1.869966 zbMATHCrossRefADSGoogle Scholar
  22. 22.
    Piomelli, U., Ferziger, J., Moin, P., Kim, J.: New approximate boundary conditions for large eddy simulations of wall-bounded flows. Phys. Fluids A 1(6), 1061–1068 (1989)CrossRefADSGoogle Scholar
  23. 23.
    Piomelli, U., Balaras, E., Pasinato, H., Squires, K.D., Spalart, P.R.: The inner-outer layer interface in large-eddy simulations with wall-layer models. Int. J. Heat Fluid Flow 24, 538–550 (2003). doi:10.1016/S0142-727X(03)00048-1 CrossRefGoogle Scholar
  24. 24.
    Pope, B.: Turbulent Flows. Cambridge University Press, UK (2000)zbMATHGoogle Scholar
  25. 25.
    Scarano, F., Benocci, C., Riethmuller, M.L.: Pattern recognition analysis of the flow past a backward facing step. Phys. Fluids 11(12), 3808–3818 (1999). doi:10.1063/1.870240 zbMATHCrossRefADSGoogle Scholar
  26. 26.
    Schumann, U.: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404 (1975). doi:10.1016/0021-9991(75)90093-5 zbMATHCrossRefMathSciNetADSGoogle Scholar
  27. 27.
    Sous, D., Bonneton, N., Sommeria, J.: Turbulent vortex dipoles in a shallow water layer. Phys. Fluids 16(8), 2886–2898 (2004)CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Spalart, P.R.: Strategies for turbulence modeling and simulations. Int. J. Heat Fluid Flow 21, 252–263 (2000). doi:10.1016/S0142-727X(00)00007-2 CrossRefGoogle Scholar
  29. 29.
    Temmerman, L., Hadziabdic, M., Leschziner, M.A., Hanjalic, K.: A hybrid two-layer URANS-LES approach for large eddy simulation at high Reynolds numbers. Int. J. Heat Fluid Flow 26, 173–190 (2005). doi:10.1016/j.ijheatfluidflow.2004.07.006 CrossRefGoogle Scholar
  30. 30.
    Tennekes, H., Lumely, J.L.: A First Course in Turbulence. MIT-Press, Cambridge, MA (1972)Google Scholar
  31. 31.
    Uijttewaal, W.S.J., Booij, R.: Effects of shallowness on the development of free-surface mixing layers. Phys. Fluids 12(2), 392–420 (2000). doi:10.1063/1.870317 zbMATHCrossRefADSGoogle Scholar
  32. 32.
    Uijttewaal, W.S.J., Tukker, J.: Development of quasi two-dimensional structures in a shallow free-surface mixing layer. Exp. Fluids 24, 192–200 (1998). doi:10.1007/s003480050166 CrossRefGoogle Scholar
  33. 33.
    Van Prooijen, B.C., Uijttewaal, W.S.J.: A linear approach for the evolution of coherent structures in shallow mixing layers. Phys. Fluids 14(12), 4105–4114 (2002). doi:10.1063/1.1514660 CrossRefADSMathSciNetGoogle Scholar
  34. 34.
    Van Prooijen, B.C.: Shallow mixing layers. PhD-thesis Delft University of Technology, The Netherlands (2004)Google Scholar
  35. 35.
    Westbury, P.S., Dunn, D.C., Morrison, J.F.: Analysis of a stochastic backscatter model for the larg-eddy simulation of wall-bounded flow. Eur. J. Mech. BFluids 23, 737–758 (2004). doi:10.1016/j.euromechflu.2004.01.003 zbMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Bram C. van Prooijen
    • 1
  • Wim S. J. Uijttewaal
    • 2
    Email author
  1. 1.Hydraulic Engineering Section, Faculty of Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands
  2. 2.Environmental Fluid Mechanics Section, Faculty of Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands

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