Boundary-Layer Meteorology

, Volume 166, Issue 3, pp 423–448 | Cite as

Impact of the Diurnal Cycle of the Atmospheric Boundary Layer on Wind-Turbine Wakes: A Numerical Modelling Study

  • Antonia EnglbergerEmail author
  • Andreas Dörnbrack
Research Article


The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation. Idealized diurnal cycle simulations of the atmospheric boundary layer are performed with the geophysical flow solver EULAG over both homogeneous and heterogeneous terrain. Under homogeneous conditions, the diurnal cycle significantly affects the low-level wind shear and atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions changes these wind characteristics, counteracting the formation of the night-time Ekman spiral. The convective, stable, evening, and morning regimes of the atmospheric boundary layer over a homogeneous surface as well as the convective and stable regimes over a heterogeneous surface are used to study the flow in a wind-turbine wake. Synchronized turbulent inflow data from the idealized atmospheric boundary-layer simulations with periodic horizontal boundary conditions are applied to the wind-turbine simulations with open streamwise boundary conditions. The resulting wake is strongly influenced by the stability of the atmosphere. In both cases, the flow in the wake recovers more rapidly under convective conditions during the day than under stable conditions at night. The simulated wakes produced for the night-time situation completely differ between heterogeneous and homogeneous surface conditions. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. Furthermore, there are different wake deflections over the height of the rotor, which reflect the incoming wind direction.


Atmospheric boundary layer Diurnal cycle Large-eddy simulation Turbulence Wind-turbine wake 



This research was performed as part of the LIPS project, funded by the Federal Ministry of Economic Affairs and Energy by a resolution of the German Federal Parliament (support code 0325518). The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, Funding was provided by Deutsches Zentrum für Luft- und Raumfahrt.


  1. Abkar M, Porté-Agel F (2014) The effect of atmospheric stability on wind-turbine wakes: a large-eddy simulation study. J Phys Conf Ser 524(1):012,138CrossRefGoogle Scholar
  2. Abkar M, Sharifi A, Porté-Agel F (2016) Wake flow in a wind farm during a diurnal cycle. J Turbul 17(4):420–441CrossRefGoogle Scholar
  3. Aitken ML, Kosović B, Mirocha JD, Lundquist JK (2014) Large eddy simulation of wind turbine wake dynamics in the stable boundary layer using the Weather Research and Forecasting Model. J Renew Sustain Energy 6(3):033,137CrossRefGoogle Scholar
  4. Baker RW, Walker SN (1984) Wake measurements behind a large horizontal axis wind turbine generator. Sol Energy 33(1):5–12CrossRefGoogle Scholar
  5. Balsley BB, Svensson G, Tjernström M (2008) On the scale-dependence of the gradient Richardson number in the residual layer. Boundary-Layer Meteorol 127(1):57–72CrossRefGoogle Scholar
  6. Basu S, Vinuesa JF, Swift A (2008) Dynamic LES modeling of a diurnal cycle. J Appl Meteorol Clim 47(4):1156–1174CrossRefGoogle Scholar
  7. Beare RJ (2008) The role of shear in the morning transition boundary layer. Boundary-Layer Meteorol 129(3):395–410CrossRefGoogle Scholar
  8. Beare RJ, Macvean MK, Holtslag AAM, Cuxart J, Esau I, Golaz JC, Jimenez MA, Khairoutdinov M, Kosović B, Lewellen D, Lund TS, Lundquist JK, Mccabe A, Moene AF, Noh Y, Raasch S, Sullivan P (2006) An intercomparison of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol 118(2):247–272CrossRefGoogle Scholar
  9. Belcher S, Jerram N, Hunt J (2003) Adjustment of a turbulent boundary layer to a canopy of roughness elements. J Fluid Mech 488:369–398CrossRefGoogle Scholar
  10. Bhaganagar K, Debnath M (2014) Implications of stably stratified atmospheric boundary layer turbulence on the near-wake structure of wind turbines. Energies 7(9):5740–5763CrossRefGoogle Scholar
  11. Bhaganagar K, Debnath M (2015) The effects of mean atmospheric forcings of the stable atmospheric boundary layer on wind turbine wake. J Renew Sustain Energy 7(1):013,124CrossRefGoogle Scholar
  12. Blay-Carreras E, Pino D, Vilà-Guerau de Arellano J, van de Boer A, De Coster O, Darbieu C, Hartogensis O, Lohou F, Lothon M, Pietersen H (2014) Role of the residual layer and large-scale subsidence on the development and evolution of the convective boundary layer. Atmos Chem Phys 14(9):4515–4530CrossRefGoogle Scholar
  13. Bou-Zeid E, Meneveau C, Parlange MB (2004) Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour Res 40(2):W02505Google Scholar
  14. Calaf M, Meneveau C, Meyers J (2010) Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys Fluids 22(1):015,110CrossRefGoogle Scholar
  15. Calaf M, Higgins C, Parlange MB (2014) Large wind farms and the scalar flux over an heterogeneously rough land surface. Boundary-Layer Meteorol 153(3):471–495CrossRefGoogle Scholar
  16. Carlson MA, Stull RB (1986) Subsidence in the nocturnal boundary layer. J Clim Appl Meteorol 25(8):1088–1099CrossRefGoogle Scholar
  17. Chamorro LP, Porté-Agel F (2010) Effects of thermal stability and incoming boundary-layer flow characteristics on wind-turbine wakes: a wind-tunnel study. Boundary-Layer Meteorol 136(3):515–533CrossRefGoogle Scholar
  18. Conzemius R, Fedorovich E (2007) Bulk models of the sheared convective boundary layer: evaluation through large eddy simulations. J Atmos Sci 64(3):786–807CrossRefGoogle Scholar
  19. Deardorff JW (1974a) Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Boundary-Layer Meteorol 7(1):81–106CrossRefGoogle Scholar
  20. Deardorff JW (1974b) Three-dimensional numerical study of turbulence in an entraining mixed layer. Boundary-Layer Meteorol 7(2):199–226CrossRefGoogle Scholar
  21. Dörenkämper M, Witha B, Steinfeld G, Heinemann D, Kühn M (2015) The impact of stable atmospheric boundary layers on wind-turbine wakes within offshore wind farms. J Wind Eng Indust Aerodyn 144:146–153CrossRefGoogle Scholar
  22. Dörnbrack A, Schumann U (1993) Numerical simulation of turbulent convective flow over wavy terrain. Boundary-Layer Meteorol 65(4):323–355CrossRefGoogle Scholar
  23. Doyle JD, Gaberšek S, Jiang Q, Bernardet L, Brown JM, Dörnbrack A, Filaus E, Grubišic V, Kirshbaum DJ, Knoth O, Koch S (2011) An intercomparison of T-REX mountain-wave simulations and implications for mesoscale predictability. Mon Weather Rev 139:2811–2831CrossRefGoogle Scholar
  24. Emeis S (2013) Wind energy meteorology: atmospheric physics for wind power generation. Springer, Berlin, HeidelbergCrossRefGoogle Scholar
  25. Emeis S (2014) Current issues in wind energy meteorology. Meteorol Appl 21(4):803–819CrossRefGoogle Scholar
  26. Englberger A, Dörnbrack A (2017) Impact of neutral boundary-layer turbulence on wind-turbine wakes: a numerical modelling study. Boundary-Layer Meteorol 162:427–449CrossRefGoogle Scholar
  27. Fedorovich E, Nieuwstadt F, Kaiser R (2001) Numerical and laboratory study of a horizontally evolving convective boundary layer. Part I: transition regimes and development of the mixed layer. J Atmos Sci 58(1):70–86CrossRefGoogle Scholar
  28. Fröhlich J (2006) Large Eddy simulation turbulenter Strömungen. Teubner Verlag/GWV Fachverlage GmbH, Wiesbaden, 414 ppGoogle Scholar
  29. Gisinger S, Dörnbrack A, Schröttle J (2015) A modified Darcy’s Law. Theor Comput Fluid Dyn 29(4):343CrossRefGoogle Scholar
  30. Gomes VMMGC, Palma JMLM, Lopes AS (2014) Improving actuator disk wake model. In: The science of making torque from wind. Conference series, vol 524, p 012170Google Scholar
  31. Grimsdell AW, Angevine WM (2002) Observations of the afternoon transition of the convective boundary layer. J Appl Meteorol 41(1):3–11CrossRefGoogle Scholar
  32. Hancock P, Zhang S (2015) A wind-tunnel simulation of the wake of a large wind turbine in a weakly unstable boundary layer. Boundary-Layer Meteorol 156(3):395–413CrossRefGoogle Scholar
  33. Hancock PE, Pascheke F (2014) Wind-tunnel simulation of the wake of a large wind turbine in a stable boundary layer: part 2, the wake flow. Boundary-Layer Meteorol 151(1):23–37CrossRefGoogle Scholar
  34. Hansen KS, Barthelmie RJ, Jensen LE, Sommer A (2012) The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at Horns Rev wind farm. Wind Energy 15(1):183–196CrossRefGoogle Scholar
  35. Iungo GV, Porté-Agel F (2014) Volumetric lidar scanning of wind turbine wakes under convective and neutral atmospheric stability regimes. J Atmos Ocean Technol 31(10):2035–2048CrossRefGoogle Scholar
  36. Kang SL, Lenschow DH (2014) Temporal evolution of low-level winds induced by two-dimensional mesoscale surface heat-flux heterogeneity. Boundary-Layer Meteorol 151(3):501–529CrossRefGoogle Scholar
  37. Kang SL, Lenschow D, Sullivan P (2012) Effects of mesoscale surface thermal heterogeneity on low-level horizontal wind speeds. Boundary-Layer Meteorol 143(3):409–432CrossRefGoogle Scholar
  38. Kataoka H, Mizuno M (2002) Numerical flow computation around aeroelastic 3D square cylinder using inflow turbulence. Wind Struct 5:379–392CrossRefGoogle Scholar
  39. Kelley CL, Ennis BL (2016) Swift site atmospheric characterization. Technical report, Sandia National Laboratories (SNL-NM), Albuquerque, NMGoogle Scholar
  40. Kühnlein C, Smolarkiewicz PK, Dörnbrack A (2012) Modelling atmospheric flows with adaptive moving meshes. J Comput Phys 231(7):2741–2763CrossRefGoogle Scholar
  41. Kumar V, Kleissl J, Meneveau C, Parlange MB (2006) Large-eddy simulation of a diurnal cycle of the atmospheric boundary layer: atmospheric stability and scaling issues. Water Resour Res 42(6):W06D09Google Scholar
  42. Lu H, Porté-Agel F (2011) Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer. Phys Fluids 23(6):065,101CrossRefGoogle Scholar
  43. Magnusson M, Smedman A (1994) Influence of atmospheric stability on wind turbine wakes. Wind Eng 18(3):139–152Google Scholar
  44. Mahrt L (1998) Nocturnal boundary-layer regimes. Boundary-Layer Meteorol 88(2):255–278CrossRefGoogle Scholar
  45. Margolin LG, Smolarkiewicz PK, Sorbjan Z (1999) Large-eddy simulations of convective boundary layers using nonoscillatory differencing. Phys D Nonlinear Phenom 133(1):390–397CrossRefGoogle Scholar
  46. Medici D, Alfredsson PH (2006) Measurements on a wind turbine wake: 3D effects and bluff body vortex shedding. Wind Energy 9(3):219–236CrossRefGoogle Scholar
  47. Millward-Hopkins J, Tomlin A, Ma L, Ingham D, Pourkashanian M (2012) The predictability of above roof wind resource in the urban roughness sublayer. Wind Energy 15(2):225–243CrossRefGoogle Scholar
  48. Mirocha JD, Kosović B, Aitken ML, Lundquist JK (2014) Implementation of a generalized actuator disk wind turbine model into the Weather Research and Forecasting model for large-eddy simulation applications. J Renew Sustain Energy 6(1):013,104CrossRefGoogle Scholar
  49. Mirocha JD, Rajewski DA, Marjanovic N, Lundquist JK, Kosović B, Draxl C, Churchfield MJ (2015) Investigating wind turbine impacts on near-wake flow using profiling lidar data and large-eddy simulations with an actuator disk model. J Renew Sustain Energy 7(4):043,143CrossRefGoogle Scholar
  50. Moeng CH, Sullivan PP (1994) A comparison of shear-and buoyancy-driven planetary boundary layer flows. J Atmos Sci 51(7):999–1022CrossRefGoogle Scholar
  51. Naughton JW, Heinz S, Balas M, Kelly R, Gopalan H, Lindberg W, Gundling C, Rai R, Sitaraman J, Singh M (2011) Turbulence and the isolated wind turbine. In: 6th AIAA theoretical fluid mechanics conference, Honolulu, Hawaii, pp 1–19Google Scholar
  52. Nieuwstadt FT (1984) The turbulent structure of the stable, nocturnal boundary layer. J Atmos Sci 41(14):2202–2216CrossRefGoogle Scholar
  53. Pino D, Vilà-Guerau de Arellano J, Duynkerke PG (2003) The contribution of shear to the evolution of a convective boundary layer. J Atmos Sci 60(16):1913–1926CrossRefGoogle Scholar
  54. Pino D, Jonker HJ, De Arellano JVG, Dosio A (2006) Role of shear and the inversion strength during sunset turbulence over land: characteristic length scales. Boundary-Layer Meteorol 121(3):537–556CrossRefGoogle Scholar
  55. Porté-Agel F, Lu H, Wu YT (2010) A large-eddy simulation framework for wind energy applications. In: The fifth international symposium on computational wind engineeringGoogle Scholar
  56. Prusa JM, Smolarkiewicz PK, Wyszogrodzki AA (2008) EULAG, a computational model for multiscale flows. Comput Fluids 37(9):1193–1207CrossRefGoogle Scholar
  57. Sathe A, Mann J, Barlas T, Bierbooms W, Bussel G (2013) Influence of atmospheric stability on wind turbine loads. Wind Energy 16(7):1013–1032CrossRefGoogle Scholar
  58. Schmidt H, Schumann U (1989) Coherent structure of the convective boundary layer derived from large-eddy simulations. J Fluid Mech 200:511–562CrossRefGoogle Scholar
  59. Schröttle J, Dörnbrack A (2013) Turbulence structure in a diabatically heated forest canopy composed of fractal Pythagoras trees. Theor Comput Fluid Dyn 27:337–359Google Scholar
  60. Smolarkiewicz PK, Charbonneau P (2013) EULAG, a computational model for multiscale flows: an MHD extension. J Comput Phys 236:608–623CrossRefGoogle Scholar
  61. Smolarkiewicz PK, Dörnbrack A (2008) Conservative integrals of adiabatic Durran’s equations. Int J Numer Methods Fluids 56:1513–1519CrossRefGoogle Scholar
  62. Smolarkiewicz PK, Margolin LG (1993) On forward-in-time differencing for fluids: extension to a curviliniear framework. Mon Weather Rev 121:1847–1859CrossRefGoogle Scholar
  63. Smolarkiewicz PK, Margolin LG (1998) MPDATA: a finite-difference solver for geophysical flows. J Comput Phys 140(2):459–480CrossRefGoogle Scholar
  64. Smolarkiewicz PK, Prusa JM (2002) Forward-in-time differencing for fluids: simulation of geophysical turbulence. In: Drikakis D, Geurts B (eds) Turbulent flow computation. Kluwer Academic Publishers, Boston, pp 279–312Google Scholar
  65. Smolarkiewicz PK, Prusa JM (2005) Towards mesh adaptivity for geophysical turbulence: continuous mapping approach. Int J Numer Methods Fluids 47:789–801CrossRefGoogle Scholar
  66. Smolarkiewicz PK, Pudykiewicz JA (1992) A class of semi-Lagrangian approximations for fluids. J Atmos Sci 49:2082–2096CrossRefGoogle Scholar
  67. Smolarkiewicz PK, Sharman R, Weil J, Perry SG, Heist D, Bowker G (2007) Building resolving large-eddy simulations and comparison with wind tunnel experiments. J Comput Phys 227:633–653CrossRefGoogle Scholar
  68. Sorbjan Z (1996) Effects caused by varying the strength of the capping inversion based on a large eddy simulation model of the shear-free convective boundary layer. J Atmos Sci 53(14):2015–2024CrossRefGoogle Scholar
  69. Sorbjan Z (1997) Decay of convective turbulence revisited. Boundary-Layer Meteorol 82(3):503–517CrossRefGoogle Scholar
  70. Sorbjan Z (2007) A numerical study of daily transitions in the convective boundary layer. Boundary-Layer Meteorol 123(3):365–383CrossRefGoogle Scholar
  71. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic, DordechtCrossRefGoogle Scholar
  72. Sullivan PP, Moeng CH, Stevens B, Lenschow DH, Mayor SD (1998) Structure of the entrainment zone capping the convective atmospheric boundary layer. J Atmos Sci 55(19):3042–3064CrossRefGoogle Scholar
  73. Tian W, Ozbay A, Yuan W, Sarakar P, Hu H (2013) An experimental study on the performances of wind turbines over complex terrain. In: 51st AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 07–10 January 2013, Grapevine, Texas, USA, pp 1–14Google Scholar
  74. Vanderwende B, Lundquist JK (2012) The modification of wind turbine performance by statistically distinct atmospheric regimes. Environ Res Lett 7(3):034,035CrossRefGoogle Scholar
  75. Vollmer L, Steinfeld G, Heinemann D, Kühn M (2016) Estimating the wake deflection downstream of a wind turbine in different atmospheric stabilities: an LES study. Wind Energy Sci 1(2):129–141CrossRefGoogle Scholar
  76. von Larcher T, Dörnbrack A (2014) Numerical simulations of baroclinic driven flows in a thermally driven rotating annulus using the immersed boundary method. Meteorol Z 23:599–610Google Scholar
  77. Wedi NP, Smolarkiewicz PK (2004) Extending Gal-Chen and Somerville terrain-following coordinate transformation on time-dependent curvilinear boundaries. J Comput Phys 193:1–20CrossRefGoogle Scholar
  78. Wedi NP, Smolarkiewicz PK (2006) Direct numerical simulation of the Plumb–McEwan laboratory analog of the QBO. J Atmos Sci 63:3226–3252CrossRefGoogle Scholar
  79. Wehner B, Siebert H, Ansmann A, Ditas F, Seifert P, Stratmann F, Wiedensohler A, Apituley A, Shaw R, Manninen H, Kulmala M (2010) Observations of turbulence-induced new particle formation in the residual layer. Atmos Chem Phys 10(9):4319–4330CrossRefGoogle Scholar
  80. Wharton S, Lundquist JK (2012) Atmospheric stability affects wind turbine power collection. Environ Res Lett 7(1):014,005CrossRefGoogle Scholar
  81. Wieringa J (1976) An objective exposure correction method for average wind speeds measured at a sheltered location. Q J R Meteorol Soc 102(431):241–253CrossRefGoogle Scholar
  82. Witha B, Steinfeld G, Heinemann D (2014) Wind energy—impact of turbulence, vol Spring 2012, Oldenburg, Germany, Springer, chap High-resolution offshore wake simulations with the LES model PALM, pp 175–181Google Scholar
  83. Wu YT, Porté-Agel F (2011) Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol 138:345–366CrossRefGoogle Scholar
  84. Wu YT, Porté-Agel F (2012) Atmospheric turbulence effects on wind-turbine wakes: an LES study. Energies 5(12):5340–5362CrossRefGoogle Scholar
  85. Zhang W, Markfort CD, Porté-Agel F (2012) Near-wake flow structure downwind of a wind turbine in a turbulent boundary layer. Exp Fluids 52:1219–1235CrossRefGoogle Scholar
  86. Zhang W, Markfort CD, Porté-Agel F (2013) Wind-turbine wakes in a convective boundary layer: a wind-tunnel study. Boundary-Layer Meteorol 146:161–179CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Institut für Physik der AtmosphäreDLR OberpfaffenhofenWeßlingGermany

Personalised recommendations