Boundary-Layer Meteorology

, Volume 173, Issue 2, pp 193–222 | Cite as

Large-Eddy Simulation of Erosion and Deposition over Multiple Two-Dimensional Gaussian Hills in a Turbulent Boundary Layer

  • G. Huang
  • C. Le RibaultEmail author
  • I. Vinkovic
  • S. Simoëns
Research Article


We investigate the effects of one or more hills on the solid-particle saltation layer, and focus on the effect of the recirculation zone that plays an important role in solid-particle erosion or entrapment. The aerodynamic features of the flow have been presented previously (Huang et al. in Environ Fluid Mech 18:581–609, 2018) and the influence of hill separation was discussed in light of the classification deduced from the urban canopy scheme of Oke (Energy Build 11:103–113, 1988). Here, large-eddy simulations (LES) coupled with Lagrangian tracking of solid particles over multiple two-dimensional Gaussian hills in a turbulent boundary layer are performed using the atmospheric Advanced Regional Prediction System. Models for the interaction of particles with the soil are used, especially for take-off and rebound, and the boundary layer at different external velocities is first simulated. Numerical results are compared with experiments performed in our laboratory (Simoëns et al. in Procedia IUTAM 17:110–118, 2015) to collect particle concentration and velocity profiles, with the different forces acting on the particles at the wall analyzed. Accumulation and erosion zones are investigated regarding the shear velocity, and different fluxes as function of the Shields number are defined and discussed. Lower momentum transfer and exchange between the recirculation region and the mixing zone in the wake-flow regime result in an increase in the number of trapped particles compared with the skimming-flow regime.


Lagrangian tracking Particle trapping Recirculation zones Solid particles Shields number 



We acknowledge NFSC/ANR Chinese/French program PEDO-COTESOF. This work was granted access to the HPC resources of CINES. Numerical simulations were also performed on the P2CHPD parallel cluster.


  1. Aguirre C, Brizuela AB, Vinkovic I, Simoëns S (2006) A subgrid Lagrangian stochastic model for turbulent passive and reactive scalar dispersion. Heat Fluid Flow 27:627–635CrossRefGoogle Scholar
  2. Almeida GP, Durao DFG, Heitor MV (1993) Wake flows behind two-dimensional model hills. Exp Therm Fluid Sci 7:87–101CrossRefGoogle Scholar
  3. Anderson RS, Haff PK (1991) Wind modification and bed response during saltation of sand in air, Aeolian Grain Transport 1. Springer, Vienna, pp 21–51Google Scholar
  4. Bagnold RA (1941) The physics of wind blown sand and desert dunes. Methuen, LondonGoogle Scholar
  5. Basu S, Lacser A (2017) A cautionary note on the use of Monin–Obukhov similarity theory in very high-resolution large-eddy simulations. Boundary-Layer Meteorol 163:344–351CrossRefGoogle Scholar
  6. Beladjine D, Ammi M, Oger L, Valance A (2007) Collision process between an incident bed and a three-dimensional granular packing. Phys Rev E 75:061305CrossRefGoogle Scholar
  7. Boëdec T, Simoëns S (2001) Simultaneous velocity and concentration measurements using Mie scattering and particle image velocimetry in a turbulent air jet, simultaneous velocity and concentration measurements using Mie scattering and particle image velocimetry in a turbulent air jet. Exp Fluids 16(3):273–281Google Scholar
  8. 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
  9. Casulli V, Cheng RT (1992) Semi-implicit finite difference methods for the three-dimensional shallow water flow. Int J Numer Methods Fluids 15:629–648CrossRefGoogle Scholar
  10. Chapman C, Walker IJ, Hesp PA, Bauer BO, Davidson-Arnott RGD, Oller-head J (2013) Reynolds stress and sand transport over a foredune. Earth Surf Process Landf 38:1735–1747CrossRefGoogle Scholar
  11. Claudin P, Wiggs GFS, Andreotti B (2013) Field evidence for the upwind velocity shift at the rest of low dunes. Boundary-Layer Meteorol 148:195–206CrossRefGoogle Scholar
  12. Clift R, Grace JR, Weber ME (1978) Bubbles, drops and particles. Academic Press, New YorkGoogle Scholar
  13. Creyssels M, Dupont P, El Moctar Ould, Valance A, cantat A, Jenkins JT, Pasini JM, Rasmussen KR (2009) Saltating particles in a turbulent boundary layer: experiment and theory. J Fluid Mech 625:47–28CrossRefGoogle Scholar
  14. Descamps I, Harion JL, Baudoin B (2005) Taking-off model of particles with a wide size distribution. Chem Eng Process 44:159–166CrossRefGoogle Scholar
  15. Diplat P, Dancey CL (2013) Coherent flow structures, initiation of motion, sediment transport and morphological feedbacks in rivers. In: Venditti JG, Best JL, Church M, Hardy RJ (eds) Coherent structures at earth’s surface. Wiley, Chichester, pp 289–307CrossRefGoogle Scholar
  16. Dupont S, Bergametti G, Marticorena B, Simoëns S (2013) Modeling saltation intermittency. J Geophys Res Atmos 118:7109–7128CrossRefGoogle Scholar
  17. Dupont S, Bergametti G, Simoëns S (2014) Modeling aeolian erosion in presence of vegetation. J Geophys Res Earth Surf 119:168–187CrossRefGoogle Scholar
  18. Durán O, Claudin P, Andreotti B (2011) On aeolian transport: grain-scale interactions, dynamical mechanisms and scaling laws. Aeolian Res 3:243–270CrossRefGoogle Scholar
  19. Dwivedi A, Melville B, Shamseldin AY (2010) Hydrodynamic forces generated on a spherical sediment particle during entrainment. J Hydraul Eng 136:756–769CrossRefGoogle Scholar
  20. Elghobashi S (1994) On the predicting particle-laden turbulent flows. App Sci Res 52:309–329CrossRefGoogle Scholar
  21. Fackrell JE, Robins AG (1982) Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. J Fluid Mech 117:1–26CrossRefGoogle Scholar
  22. Foucaut JM, Stanislas M (1996) Take-off threshold velocity of solid particles lying under a turbulent boundary layer. Exp Fluids 20:377–382CrossRefGoogle Scholar
  23. Gore R, Crowe CT (1989) Effect of particle size on modulating turbulent intensity. Int J Multiph Flow 15(2):279–285CrossRefGoogle Scholar
  24. Hofland B, Batjes JA, Booij R (2005) Measurement of fluctuating pressures on coarse bed material. J Hydraul Eng 131(9):770–781CrossRefGoogle Scholar
  25. Huang G (2015) Numerical simulation of solid particle transport in atmospheric boundary-layer over obstacles, Thèse Ecole Centrale de LyonGoogle Scholar
  26. Huang G, Simoëns S, Vinkovic I, Le Ribault C, Dupont S, Bergametti G (2016) Law-of-the-wall in a boundary-layer over regularly distributed roughness elements. J Turbul 17:1–24CrossRefGoogle Scholar
  27. Huang G, Simoëns S, Vinkovic I, Le Ribault C (2018) Part I A priori study of erosion and deposition with large eddy simulation of turbulent flow over multiple 2D sandy Gaussian hills. Environ Fluid Mech 18(3):581–609CrossRefGoogle Scholar
  28. Jackson PS, Hunt JCR (1975) Turbulent wind flow over a low hill. Q J R Meteorol Soc 101:929–955CrossRefGoogle Scholar
  29. Kok JF, Renno N (2009) A comprehensive numerical model of steady state saltation (COMSALT). J Geophys Res Atmos 114:17204CrossRefGoogle Scholar
  30. Le Ribault C, Vignon JM, Simoëns S (2014) LES/Lagrangian modelling for the dispersion of reactive species behind an obstacle in a turbulent boundary layer. JP J Heat Mass Transf 9(1):21–55Google Scholar
  31. Lund T, Wu X, Squires K (1998) Generation of turbulent inflow data for spatially developing boundary layer simulations. J Comput Phys 140:233–258CrossRefGoogle Scholar
  32. Mollinger AM, Nieuwstadt FTM (1996) Measurement of the lift force on a particle fixed to the wall in the viscous sublayer of a fully developed turbulent boundary layer. J Fluid Mech 316:285–306CrossRefGoogle Scholar
  33. Nabi M, de Vriend HJ, Mosselman E, Sloff CJ, Shimizu Y (2013a) Detailed simulation of morphodynamics: 2 Sediment pickup, transport and deposition. Water Resour Res 49:1–17CrossRefGoogle Scholar
  34. Nabi M, de Vriend HJ, Mosselman E, Sloff CJ, Shimizu Y (2013b) Detailed simulation of morphodynamics: 3 Ripples and dunes. Water Resour Res 49:5930–5943CrossRefGoogle Scholar
  35. Nabi M, de Vriend HJ, Mosselman E, Sloff CJ, Shimizu Y (2012) Detailed simulation of morphodynamics: 1 Hydrodynamic model. Water Resour Res 48:
  36. Ohba R, Hara T, Nakamura S, Ohya Y, Uchida T (2002) Gas diffusion over an isolated hill under neutral, stable and unstable conditions. Atmos Environ 36:5697–5707CrossRefGoogle Scholar
  37. Oke TR (1988) Street design and urban canopy layer climate. Energy Build 11:103–113CrossRefGoogle Scholar
  38. Owen PR (1964) Saltation of uniform grains in air. J Fluid Mech 20:225–242CrossRefGoogle Scholar
  39. Sardina G, Picano F, Schlatter P, Brandt L, Casciola CM (2014) Statistics of particle accumulation in spatially developing turbulent boundary layers. Flow Turbul Combust 92(1–2):27–40CrossRefGoogle Scholar
  40. Schmeeckle MW, Nelson JM, Shreve RL (2007) Forces on stationary particles in near-bed turbulent flows. J Geophys Res Earth Surf 112:F02003CrossRefGoogle Scholar
  41. Shao Y (2009) Physics and modeling of wind erosion, 37, Atmospheric and Oceanographic Sciences Library, Springer Netherlands, DordrechtGoogle Scholar
  42. Shao Y, Li A (1999) Numerical modelling of saltation in the atmospheric surface layer. Boundary-layer Meteorol 91:199–225CrossRefGoogle Scholar
  43. Shields A (1936) Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen des Versuchsanstalt fur Wasserbau and Shiffbau 26:101Google Scholar
  44. Simoëns S, Wallace JM (2008) The flow across a street canyon of variable width—part 2: scalar dispersion for the flow across a street canyon of variable width. Atmos Environ 42(10):2489–2503CrossRefGoogle Scholar
  45. Simoëns S, Ayrault M, Wallace J (2007) The flow across a street canyon of variable width—part 1: kinematic description. Atmos Environ 41:9002–9017CrossRefGoogle Scholar
  46. Simoëns S, Saleh S, Le Ribault C, Belmadi M, Zegadi R, Allag F, Vignon JM, Huang G (2015) Influence of Gaussian hill on concentration of solid particles in suspension inside Turbulent Boundary Layer. Procedia IUTAM 17:110–118CrossRefGoogle Scholar
  47. Sorensen M (1991) An analytic model of wind-blown sand transport Acta Mechanica Supplementum. Springer, Vienna, pp 67–81Google Scholar
  48. Spalart PR (1988) Direct simulation of a turbulent boundary layer up to R\(\theta \)=1410. J Fluid Mech 187:61–98CrossRefGoogle Scholar
  49. Spalding DB (1961) A single formula for the “law of wall”. J Appl Mech 28:455CrossRefGoogle Scholar
  50. Sumer BM, Chua L, Cheng NS (2003) Influence of turbulence on bed load sediment transport. J Hydraul Eng 129:585–596CrossRefGoogle Scholar
  51. Taylor PA, Mason PJ, Bradley EF (1987) Boundary-layer flow over low hills–a review. Boundary-Layer Meteorol 39:107–132CrossRefGoogle Scholar
  52. Vinçont JY, Simoëns S, Ayrault M, Wallace JM (2000) Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and down stream of an obstacle. J Fluid Mech 424:127–167CrossRefGoogle Scholar
  53. Vinkovic (2005) Dispersion et mélange turbulents de particules solides et de gouttelettes par une simulation des grandes échelles et une modélisation stochastique lagrangienne. Application à la pollution de l’atmosphère. Thèse Ecole Centrale de Lyon Google Scholar
  54. Vinkovic I, Aguirre C, Simoëns S, Ayrault M (2006a) Large eddy simulation of the dispersion of solid particles in a turbulent boundary layer. Boundary-Layer Meteorol 121:283–311CrossRefGoogle Scholar
  55. Vinkovic I, Aguirre C, Simoëns S (2006b) Large eddy simulation and Lagrangian stochastic modeling of passive scalar dispersion in a turbulent boundary layer. J Turbul 7(30). CrossRefGoogle Scholar
  56. Wallace JM, Eckelmann H, Brodkey RS (1972) Structure of the Reynolds stress near the wall. J Fluid Mech 54:65–92CrossRefGoogle Scholar
  57. Wang Z, Huang N (2017) Numerical simulation of the falling snow deposition over complex terrain. J Geophys Atmos 122(2):980–1000CrossRefGoogle Scholar
  58. Weng WS, Hunt JCR, Carruthers DJ, Warren A, Wiggs GFS, Livingstone I, Castro I (1991) Air flow and sand transport over sand-dunes. Acta Mech Suppl 2:1–22CrossRefGoogle Scholar
  59. Wood N (1995) The onset of separation in neutral, turbulent flow over hills. Boundary-Layer Meteorol 76:137–164CrossRefGoogle Scholar
  60. Xue M, Droegemeier K, Wong V, Shapiro A, Brewster K (1995) ARPS version 4.0 Users GuideGoogle Scholar
  61. Xu B, Zhang J, Huang N, Gong K, Liu Y (2018) Characteristics of turbulent aeolian sand movement over straw checkerboard barriers and formation mechanisms of their internal erosion form. J Geophys Res Atmos (online)Google Scholar
  62. Yamamoto Y, Potthoff M, Tanaka T, Kashijima T, Tsuji Y (2001) Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effects of considering inter-particle collisions. J Fluid Mech 442:303–334CrossRefGoogle Scholar
  63. Yoshizawa A, Horiuti K (1995) A statistically-derived subgrid-scale kinetic models for large eddy simulation of turbulent. J Phys Soc Jpn 54(8):2834–2839CrossRefGoogle Scholar
  64. Zimon AD (1969) Adhesion of dust and powder. Springer, DordrechtCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • G. Huang
    • 1
  • C. Le Ribault
    • 1
    Email author
  • I. Vinkovic
    • 1
  • S. Simoëns
    • 1
  1. 1.LMFA, ECL, CNRS UMR 5509, INSA Lyon, UCB Lyon 1Ecully CedexFrance

Personalised recommendations