Boundary-Layer Meteorology

, Volume 170, Issue 3, pp 415–441 | Cite as

Large-Eddy Simulations of the Flow Over an Isolated Three-Dimensional Hill

  • Zhenqing Liu
  • Shuyang Cao
  • Heping LiuEmail author
  • Takeshi Ishihara
Research Article


Atmospheric three-dimensional (3D) mean and turbulent flow over an isolated 3D hill of cosine-squared cross-section and a smooth surface are studied by large-eddy simulations validated against data from a wind-tunnel experiment. Many features of the 3D flow across the hill are identified through analyzing mean and turbulent quantities on three surfaces, including a vertical cross-section across the hilltop, and surfaces of vertical distances of 0.25h and 1.25h from the ground, where h is the hill height. Besides flow blocking and separation with a recirculation region immediately upstream and downstream of the hill, respectively, a spiral-shaped structure wandering in both the lateral and vertical directions develops, accompanied by the wake and shear regions where sweep and ejection events play different roles in momentum transfer. The secondary rotations in the wake flow as well as the inner and outer rotations associated with the core vortex are also identified, together with other features.


Coherent structures Large-eddy simulations Mean and turbulent flow Three-dimensional hill 



Z. Liu acknowledges the support by the National Key Research and Development Plan of China (2016YFE0127900 and 2016YFC0800206), the National Natural Science Foundations of China (51608220), and the Project of Innovation-driven Plan in Huazhong University of Science and Technology (2017KFYXJJ141). S. Cao acknowledges support by the National Natural Science Foundations of China (51720105005). H. Liu acknowledges support by the National Science Foundation (NSF-AGS-1419614).


  1. Ansys Inc (2014) Ansys fluent 14.0 user’s. Guide, U.SGoogle Scholar
  2. Baker CJ (2010) The simulation of unsteady aerodynamic cross wind forces on trains. J Wind Eng Ind Aerodyn 98:88–99CrossRefGoogle Scholar
  3. Bédard J, Yu W, Gagnon Y, Masson C (2013) Development of a geophysic model output statistics module for improving short-term numerical wind predictions over complex sites. Wind Energy 16:1131–1147Google Scholar
  4. Cao S, Tamura T (2006) Experimental study on roughness effects on turbulent boundary layer flow over a two-dimensional steep hill. J Wind Eng Ind Aerodyn 94:1–19CrossRefGoogle Scholar
  5. Carvalho AC, Carvalho A, Gelpi I, Barreiro M, Borrego C, Miranda AI, Pérez-Muñuzuri V (2006) Influence of topography and land use on pollutants dispersion in the atlantic coast of iberian peninsula. Atmos Environ 40:3969–3982CrossRefGoogle Scholar
  6. Castro FA, Silva C, Lopes C (2014) One-way mesoscale–microscale coupling for the simulation of atmospheric flows over complex terrain. Wind Energy 18:1251–1272CrossRefGoogle Scholar
  7. Courant R, Friedrichs K, Lewy H (1928) Über die partiellen differenzengleichungen der mathematischen physik. Math Annal 100:32–74CrossRefGoogle Scholar
  8. Davenport AG, King J (1990) The influence of topography on the dynamic wind loading of long span bridges. J Wind Eng Ind Aerodyn 36:1373–1382CrossRefGoogle Scholar
  9. DeLeon R, Sandusky M, Senocak I (2018) Simulations of turbulent flow over complex terrain using an immersed-boundary method. Boundary-Layer Meteorol 167:399–420CrossRefGoogle Scholar
  10. Dupont S, Brunet Y (2008) Edge flow and canopy structure: a large-eddy simulation study. Boundary-Layer Meteorol 126:51–71CrossRefGoogle Scholar
  11. Ferziger JH, Peric M (2002) Computational method for fluid dynamics. Springer, BerlinCrossRefGoogle Scholar
  12. Gong W, Ibbetson A (1989) A wind tunnel study of turbulent flow over model hills. Boundary-Layer Meteorol 49:113–148CrossRefGoogle Scholar
  13. Gong W, Taylor PA, Dornbrack A (1996) Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves. J Fluid Mech 312:1–37CrossRefGoogle Scholar
  14. Hancock PE, Hayden P (2018) Wind-tunnel simulation of weakly and moderately stable atmospheric boundary layers. Boundary-Layer Meteorol 168:29–57CrossRefGoogle Scholar
  15. Hunt J, Carruthers D (1990) Rapid distortion theory and the ‘problems’ of turbulence. J Fluid Mech 212:497–532CrossRefGoogle Scholar
  16. Iizuka S, Kondo H (2004) Performance of various sub-grid scale models in large-eddy simulations of turbulent flow over complex terrain. Atmos Environ 38:7083–7091CrossRefGoogle Scholar
  17. Iizuka S, Kondo H (2006) Large-eddy simulations of turbulent flow over complex terrain using modified static eddy viscosity models. Atmos Environ 40:925–935CrossRefGoogle Scholar
  18. Ishihara T, Hibi K (1998) An experimental study of turbulent boundary layer over steep hills. In: Proceedings of the 15th national symposium on wind engineering, Japan, pp 61–66Google Scholar
  19. Ishihara T, Oikawa S, Hibi K (1999) Wind tunnel study of turbulent flow over a three-dimensional steep hill. J Wind Eng Ind Aerodyn 83:95–107CrossRefGoogle Scholar
  20. Ishihara T, Fujino Y, Hibi K (2001) A wind tunnel study of separated flow over a two-dimensional ridge and a circular hill. J Wind Eng 89:573–576Google Scholar
  21. Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows. Oxford University Press, OxfordGoogle Scholar
  22. Kutter E, Yi C, Hendrey G, Liu H, Eaton T, Ni-Meister W (2017) Recirculation over complex terrain. J Geophys Res Atmos 122:6637–6651CrossRefGoogle Scholar
  23. Liu Z, Ishihara T, Tanaka T, He X (2016) LES study of turbulent flow fields over a smooth 3D hill and a smooth 2-D ridge. J Wind Eng Ind Aerodyn 153:1–12CrossRefGoogle Scholar
  24. Lopes AMG, Cruz MG, Viegas DX (2002) Firestation—an integrated software system for the numerical simulation of fire spread on complex topography. Environ Model Softw 17:269–285CrossRefGoogle Scholar
  25. Ma Y, Liu H (2017) Large-eddy simulations of atmospheric flows over complex terrain using the immersed-boundary method in the weather research and forecasting model. Boundary-Layer Meteorol 165:421–445CrossRefGoogle Scholar
  26. Mason PJ, Thomson DJ (1987) Large-eddy simulations of the neutral-static-stability planetary boundary layer. Q J R Meteorol Soc 113:413–443CrossRefGoogle Scholar
  27. Matusick G, Ruthrof KX, Brouwers NC, Hardy GSJ (2014) Topography influences the distribution of autumn frost damage on trees in a mediterranean-type eucalyptus forest. Trees 28:1449–1462CrossRefGoogle Scholar
  28. Perdikaris GA (2001) Numerical simulation of the three-dimensional micro-scale dispersion of air-pollutants in regions with complex topography. Heat Mass Transf 37:583–591CrossRefGoogle Scholar
  29. Politis ES, Prospathopoulos J, Cabezon D, Hansen KS, Chaviaropoulos PK, Barthelmie RJ (2012) Modeling wake effects in large wind farms in complex terrain: the problem, the methods and the issues. Wind Energy 15:161–182CrossRefGoogle Scholar
  30. Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44:1–25CrossRefGoogle Scholar
  31. Şen Z (2003) A short physical note on a new wind power formulation. Renew Energy 28:2379–2382CrossRefGoogle Scholar
  32. Shaw RH, Brunet Y, Finnigan JJ, Raupach MR (1995) A wind tunnel study of air flow in waving wheat: two-point velocity statistics. Boundary-Layer Meteorol 76:349–376CrossRefGoogle Scholar
  33. Shekar A, Graham M (2018) Exact coherent states with hairpin-like vortex structure in channel flow. J Fluid Mech 849:76–89CrossRefGoogle Scholar
  34. Su HB, Shaw RH, Paw UKT (2000) Two-point correlation analysis of neutrally stratified flow within and above a forest from large-eddy simulation. Boundary-Layer Meteorol 94:423–460CrossRefGoogle Scholar
  35. Tamura T, Cao S, Okuno A (2007a) LES study of turbulent boundary layer over a smooth and a rough 2D hill model. Flow Turbul Combust 79:405–432CrossRefGoogle Scholar
  36. Tamura T, Okuno A, Sugio Y (2007b) LES analysis of turbulent boundary layer over 3D steep hill covered with vegetation. J Wind Eng Ind Aerodyn 95:1463–1475CrossRefGoogle Scholar
  37. Tian S, Gao Y, Dong X, Liu C (2018) Definitions of vortex vector and vortex. J Fluid Mech 849:312–339CrossRefGoogle Scholar
  38. Zilker D, Cook G, Hanratty T (1977) Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J Fluid Mech 82:29–51CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Zhenqing Liu
    • 1
  • Shuyang Cao
    • 2
  • Heping Liu
    • 3
    Email author
  • Takeshi Ishihara
    • 4
  1. 1.School of Civil Engineering and MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.State Key Laboratory for Disaster Reduction in Civil EngineeringTongji UniversityShanghaiChina
  3. 3.Department of Civil and Environmental EngineeringWashington State UniversityPullmanUSA
  4. 4.Department of Civil Engineering, School of EngineeringThe University of TokyoTokyoJapan

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