Boundary-Layer Meteorology

, Volume 149, Issue 2, pp 231–257 | Cite as

Improving a Two-Equation Turbulence Model for Canopy Flows Using Large-Eddy Simulation

  • A.Silva Lopes
  • J. M. L. M. Palma
  • J. Viana Lopes


Large-eddy simulations of the neutrally-stratified flow over an extended homogeneous forest were used to calibrate a canopy model for the Reynolds-averaged Navier–Stokes (RaNS) method with the \(k-\varepsilon \) turbulence model. It was found that, when modelling the forest as a porous medium, the canopy drag dissipates the turbulent kinetic energy (acts as a sink term). The proposed model was then tested in more complex flows: a finite length forest and a forested hill. In the finite length forest, the destruction of the turbulent kinetic energy by the canopy was overestimated near the edge, for a length approximately twice the tree height. In the forested hill, the model was less accurate inside the recirculation zone and overestimated the turbulent kinetic energy, due to an incorrect prediction of the production term. Nevertheless, the canopy model presented here provided consistent results in both a priori and a posteriori tests and improved the accuracy of RaNS simulations with the \(k-\varepsilon \) model.


Forest canopy \(k-\varepsilon \) turbulence model Large-eddy simulation Model calibration 



A. Silva Lopes and J. Viana Lopes are research fellows under Programa Ciência of the Portuguese Foundation for Science and Technology (FCT). These research activities were developed as part of the work program of the Center for Wind Energy and Atmospheric Studies, a unit of the Portuguese research network, sponsored by the Portuguese Foundation for Science and Technology (FCT).


  1. Ayotte K, Finnigan J, Raupach M (1999) A second-order closure for neutrally stratified vegetative canopy flows. Boundary-Layer Meteorol 90:189–216CrossRefGoogle Scholar
  2. Belcher S, Harman I, Finnigan J (2012) The wind in the willows: flows in forest canopies in complex terrain. Annu Rev Fluid Mech 44:479–504CrossRefGoogle Scholar
  3. Beljaars A, Walmsley J, Taylor P (1987) A mixed spectral finite-difference model for neutrally stratified boundary-layer flow over roughness changes and topography. Boundary-Layer Meteorol 38:273–303CrossRefGoogle Scholar
  4. Calaf M, Meneveau C, Meyers J (2010) Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys Fluids 22(015):110Google Scholar
  5. Dupont S, Brunet Y (2008) Edge flow and canopy structure: a large-eddy simulation study. Boundary-Layer Meteorol 126:51–71CrossRefGoogle Scholar
  6. Dupont S, Brunet Y (2009) Coherent structures in canopy edge flow: a large-eddy simulation study. J Fluid Mech 630:93–128CrossRefGoogle Scholar
  7. Dupont S, Patton E (2012) Influence of stability and seasonal canopy changes on micrometeorology within and above an orchard canopy: the CHATS experiment. Agric For Meteorol 157:11–29CrossRefGoogle Scholar
  8. Dupont S, Brunet Y, Finnigan J (2008) Large-eddy simulation of turbulent flow over a forested hill: validation and coherent structure identification. Q J R Meteorol Soc 134:1911–1929CrossRefGoogle Scholar
  9. Dwyer M, Patton E, Shaw R (1997) Turbulent kinetic energy budgets from a large-eddy simulation of airflow above and within a forest canopy. Boundary-Layer Meteorol 84:23–43CrossRefGoogle Scholar
  10. Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32:519–571CrossRefGoogle Scholar
  11. Finnigan J, Shaw R, Patton E (2009) Turbulence structure above a vegetation canopy. J Fluid Mech 637:387–424CrossRefGoogle Scholar
  12. Foudhil H, Brunet Y, Caltagirone JP (2005) A fine-scale \(k\)\(\varepsilon \) model for atmospheric flow over heterogeneous landscapes. Environ Fluid Mech 5:247–265CrossRefGoogle Scholar
  13. Green S (1992) Modelling turbulent air flow in a stand of widely-spaced trees. PHOENICS. J Comput Fluid Dyn Appl 5:294–312Google Scholar
  14. Harman I, Finnigan J (2007) A simple unified theory for flow in the canopy and roughness sublayer. Boundary-Layer Meteorol 123:339–363CrossRefGoogle Scholar
  15. Jones W, Launder B (1972) The prediction of laminarization with a two-equation model of turbulence. Int J Heat Mass Transf 15:301–314CrossRefGoogle Scholar
  16. Katul G, Mahrt L, Poggi D, Sanz C (2004) One- and two-equation models for canopy turbulence. Boundary-Layer Meteorol 113:81–109CrossRefGoogle Scholar
  17. Liu J, Chen J, Black T, Novak M (1996) \(E\)\(\varepsilon \) modelling of turbulent air flow downwind of a model forest edge. Boundary-Layer Meteorol 77:21–44CrossRefGoogle Scholar
  18. Mansour N, Kim J, Moin P (1988) Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J Fluid Mech 194:15–44Google Scholar
  19. Marusic I, Kunkel G, Porté-Agel F (2001) Experimental study of wall boundary conditions for large-eddy simulation. J Fluid Mech 446:309–320Google Scholar
  20. Mason P, Thomson D (1992) Stochastic backscatter in large-eddy simulations of boundary layers. J Fluid Mech 242:51–78CrossRefGoogle Scholar
  21. Meneveau C, Lund T, Cabot W (1996) A Lagrangian dynamic subgrid-scale model of turbulence. J Fluid Mech 319:353–385CrossRefGoogle Scholar
  22. Mohammadi B, Pironneau O (1994) Analysis of the K–epsilon turbulence model, 1st edn. Wiley, Hoboken, 194 ppGoogle Scholar
  23. Murakami S (1993) Comparison of various turbulence models applied to a bluff body. J Wind Eng Ind Aerodyn 46–47:21–36CrossRefGoogle Scholar
  24. Patton E, Katul G (2009) Turbulent pressure and velocity perturbations induced by gentle hills covered with sparse and dense canopies. Boundary-Layer Meteorol 133:189–217CrossRefGoogle Scholar
  25. Patton E, Horst T, Sullivan P, Lenschow D, Oncley S, Brown W, Burns S, Guenther A, Held A, Karl T, Mayor S, Rizzo L, Spuler S, Sun J, Turnipseed A, Allwine E, Edburg S, Lamb B, Avissar R, Calhoun R, Kleissl J, Massman W, Paw UK, Weil J (2011) The canopy horizontal array turbulence study. Bull Am Meteorol Soc 92:593–611CrossRefGoogle Scholar
  26. Piomelli U, Balaras E (2002) Wall-layer models for large-eddy simulations. Annu Rev Fluid Mech 34:349–374CrossRefGoogle Scholar
  27. Raupach M (1994) Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index. Boundary-Layer Meteorol 71:211–216CrossRefGoogle Scholar
  28. Raupach M, Shaw R (1982) Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol 22:79–90CrossRefGoogle Scholar
  29. Raupach M, Thom A, Edwards I (1980) A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces. Boundary-Layer Meteorol 18:373–397CrossRefGoogle Scholar
  30. Raupach M, Finnigan J, Brunei Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol 78:351–382CrossRefGoogle Scholar
  31. Sanz C (2003) A note on \(k\)-\(\varepsilon \) modelling of vegetation canopy air-flows. Boundary-Layer Meteorol 108:191–197CrossRefGoogle Scholar
  32. Shaw R, Patton E (2003) Canopy element influences on resolved- and subgrid-scale energy within a large-eddy simulation. Agric For Meteorol 115:5–17CrossRefGoogle Scholar
  33. Shaw R, Pereira A (1982) Aerodynamic roughness of a plant canopy: a numerical experiment. Agric Meteorol 26:51–65CrossRefGoogle Scholar
  34. Shaw R, Schumann U (1992) Large-eddy simulation of turbulent flow above and within a forest. Boundary-Layer Meteorol 61:47–64CrossRefGoogle Scholar
  35. Silva Lopes A, Palma J (2002) Numerical simulation of isotropic turbulence using a collocated approach and a nonorthogonal grid system. J Comput Phys 175:713–738CrossRefGoogle Scholar
  36. Silva Lopes A, Piomelli U, Palma J (2006) Large-eddy simulation of the flow in an S-duct. J Turbul 7:N11CrossRefGoogle Scholar
  37. Silva Lopes A, Palma J, Castro F (2007) Simulation of the Askervein flow. Part 2: large-eddy simulations. Boundary-Layer Meteorol 125:85–108CrossRefGoogle Scholar
  38. Sogachev A, Panferov O (2006) Modification of two-equation models to account for plant drag. Boundary-Layer Meteorol 121:229–266CrossRefGoogle Scholar
  39. Svensson U, Häggkvist K (1990) A two-equation turbulence model for canopy flows. J Wind Eng Ind Aerodyn 35:201–211CrossRefGoogle Scholar
  40. Wilson J (1988) A second-order closure model for flow through vegetation. Boundary-Layer Meteorol 42:371–392CrossRefGoogle Scholar
  41. Yang B, Morse A, Shaw R, Paw UK (2006a) Large-eddy simulation of turbulent flow across a forest edge. Part II: momentum and turbulent kinetic energy budgets. Boundary-Layer Meteorol 121:433–457CrossRefGoogle Scholar
  42. Yang B, Raupach M, Shaw R, Paw UK, Morse A (2006b) Large-eddy simulation of turbulent flow across a forest edge. Part I: flow statistics. Boundary-Layer Meteorol 120:377–412CrossRefGoogle Scholar
  43. Yue W, Parlange M, Meneveau C, Zhu W, van Hout R, Katz J (2007) Large-eddy simulation of plant canopy flows using plant-scale representation. Boundary-Layer Meteorol 124:183–203CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • A.Silva Lopes
    • 1
  • J. M. L. M. Palma
    • 1
  • J. Viana Lopes
    • 1
  1. 1.CEsAFaculdade de Engenharia, Universidade do PortoPortoPortugal

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