Boundary-Layer Meteorology

, Volume 173, Issue 3, pp 409–434 | Cite as

Turbulence Coherence Within Canonical and Realistic Aeolian Dune-Field Roughness Sublayers

  • C. Wang
  • W. AndersonEmail author
Research Article


Large-eddy simulation has been used to study the formation and spatial nature of inertia-dominated turbulent flows responding to aeolian sand dunes. The former is recovered from simulations initialized with a Reynolds-averaged flow, without any small-scale features, which highlights the emergence of salient structures within the dune-field roughness sublayer (RSL). The latter is based upon computation of integral lengths. In the interest of generality, these exercises are based upon flow over canonical dune geometries—which serve as a comparative benchmark—and flow over a section of the White Sands National Monument aeolian dune field in southern New Mexico. These cases, thus, capture a vast range of complexity. In both applications, we report the emergence of mixing-layer-like processes—as per results for other canopy flows—although the distinct geometric nature of the dunes shows the prevalence of a persistent interdune roller, which is aligned most closely with the streamwise direction. In order to demonstrate underlying similarities in the processes occuring above idealized and natural dune fields, we normalize the integral lengths by characteristic length scales: vorticity thickness, attached-eddy-hypothesis mixing length, and dissipation length. This exercise reveals a distinct growth and collapse pattern that is robust across all considered dune arrangements. Herein, ‘growth’ refers to the stage of downflow thickening of vortices produced via vortex shedding off the upflow dune; growth is regulated by the lesser of the distance to the wall or distance to the upflow dune, where the latter marks the beginning of the ‘collapse’ stage. Both are compliant with the notion of wall-attached eddies. In the RSL, we demonstrate that the integral lengths exhibit an optimal collapse when normalized by vorticity thickness, while inertial layer scaling is attained as close as one dune height above the top of the dune canopy. These results help to establish dune-field RSL dynamics within the broader context of canopy turbulence, which is important given the relatively greater efforts devoted to flows over vegetative canopies and urban environments.


Aeolian morphodynamics Roughness sublayer Surface layer 



This work was supported by the National Science Foundation, Grant # CBET 1603254. Scientific computing resources were provided by the Texas Advanced Computing Center. The idealized dune DEM was provided by Ken Christensen, Notre Dame. The White Sands National Monument DEM was provided by Gary Kocurek and David Mohrig, University of Texas at Austin.


  1. Albertson J, Parlange M (1999) Surface length scales and shear stress: implications for land-atmosphere interaction over complex terrain. Water Resour Res 35:2121–2132Google Scholar
  2. Anderson W (2012) An immersed boundary method wall model for high-reynolds number channel flow over complex topography. Int J Numer Methods Fluids 71:1588–1608Google Scholar
  3. Anderson W (2016) Amplitude modulation of streamwise velocity fluctuations in the roughness sublayer: evidence from large-eddy simulations. J Fluid Mech 789:567–588Google Scholar
  4. Anderson W, Meneveau C (2010) A large-eddy simulation model for boundary-layer flow over surfaces with horizontally resolved but vertically unresolved roughness elements. Boundary-Layer Meteorol 137:397–415Google Scholar
  5. Anderson W, Meneveau C (2011) A dynamic large-eddy simulation model for boundary layer flow over multiscale, fractal-like surfaces. J Fluid Mech 679:288–314Google Scholar
  6. Anderson W, Chamecki M (2014) Numerical study of turbulent flow over complex aeolian dune fields: The White Sands National Monument. Phys Rev E 89:013005–1–14Google Scholar
  7. Anderson W, Li Q, Bou-Zeid E (2015) Numerical simulation of flow over urban-like topographies and evaluation of turbulence temporal attributes. J Turbul 16:809–831Google Scholar
  8. Bagnold R (1956) The physics of blown sand and desert dunes. Chapman and Hall, LondonGoogle Scholar
  9. Bailey B, Stoll R (2013) Turbulence in sparse, organized vegetative canopies: a large-eddy simulation study. Boundary-Layer Meteorol. CrossRefGoogle Scholar
  10. Bailey BN, Stoll R (2016) The creation and evolution of coherent structures in plant canopy flows and their role in turbulent transport. J Fluid Mech 789:425–460Google Scholar
  11. Bou-Zeid E, Meneveau C, Parlange M (2005) A scale-dependent lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys Fluids 17(025):105Google Scholar
  12. Bristow N, Blois G, Best J, Christensen K (2018) Turbulent flow structure associated with collision between laterally offset, fixed-bed barchan dunes. J Geophys Res-Earth Surf 123(9):2157–2188Google Scholar
  13. Bristow N, Blois G, Best J, Christensen K (2019) Spatial scales of turbulent flow structures associated with interacting barchan dunes. J Geophys Res-Earth Surf. CrossRefGoogle Scholar
  14. Browand F, Troutt T (1985) The turbulent mixing layer: geometry of large vortices. J Fluid Mech 158:489–509Google Scholar
  15. Castro I (2007) Rough-wall boundary layers: mean flow universality. J Fluid Mech 585:469–485Google Scholar
  16. Charru F, Andreotti B, Claudin P (2013) Sand ripples and dunes. Annu Rev Fluid Mech 45:469–493Google Scholar
  17. Claudin P, Wiggs G, Andreotti B (2013) Field evidence for the upwind velocity shift at the crest of low dunes. Boundary-Layer Meteorol 148:195–206Google Scholar
  18. Coceal O, Dobre A, Thomas T, Belcher S (2007) Structure of turbulent flow over regular arrays of cubical roughness. J Fluid Mech 589:375–409Google Scholar
  19. Davidson P, Krogstad PÅ (2014) A universal scaling for low-order structure functions in the log-law region of smooth-and rough-wall boundary layers. J Fluid Mech 752:140–156Google Scholar
  20. Durán O, Parteli EJ, Herrmann HJ (2010) A continuous model for sand dunes: Review, new developments and application to barchan dunes and barchan dune fields. Earth Surf Proc Land 35:1591–1600 Google Scholar
  21. Ewing R, Kocurek G (2010a) Aeolian dune-field pattern boundary conditions. Geomorphology 114:175–187Google Scholar
  22. Ewing R, Kocurek G (2010b) Aeolian dune interactions and dune-field pattern formation: White Sands Dune Field, New Mexico. Sedimentology 57:1199–1218Google Scholar
  23. Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32:519–571Google Scholar
  24. Flack K, Schultz M, Connelly J (2007) Examination of a critical roughness height for outer layer similarity. Phys Fluids 19(9):095104Google Scholar
  25. Fröhlich J, Mellen C, Rodi W, Temmerman L, Leschziner M (2005) Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J Fluid Mech 526:19–66Google Scholar
  26. Gao W, Shaw R, U KP (1989) Observation of organized structure in turbulent flow within and above a forest canopy. Boundary-Layer Meteorol 47:349–377Google Scholar
  27. Germano M (1992) Turbulence: the filtering approach. J Fluid Mech 238:325–336Google Scholar
  28. Germano M, Piomelli U, Moin P, Cabot W (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids 3:1760–1765Google Scholar
  29. Ghisalberti M (2009) Obstructed shear flows: similarities across systems and scales. J Fluid Mech 641:51Google Scholar
  30. Grass A (1971) Structural features of turbulent flow over smooth and rough boundaries. J Fluid Mech 50:233–255Google Scholar
  31. Hersen P, Douady S (2005) Collision of barchan dunes as a mechanism of size regulation. Geophys Res Lett. CrossRefGoogle Scholar
  32. Hersen P, Andersen K, Elbelrhiti H, Andreotti B, Claudin P, Douady S (2004) Corridors of barchan dunes: stability and size selection. Phys Rev E 69(011):304Google Scholar
  33. Hutchins N, Marusic I (2007) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28Google Scholar
  34. Jackson P, Hunt J (1975) Turbulent flow over a low hill. Q J R Meteorol Soc 101:929–955Google Scholar
  35. Jacob C, Anderson W (2016) Conditionally averaged large-scale motions in the neutral atmospheric boundary layer: insights for aeolian processes. Boundary-Layer Meteorol 162:21–41Google Scholar
  36. Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94Google Scholar
  37. Jerolmack D, Mohrig D (2005) A unified model for subaqueous bed form dynamics. Water Resour Res. CrossRefGoogle Scholar
  38. Jerolmack D, Ewing R, Falcini F, Martin R, Masteller C, Phillips C, Reitz M, Buynevich I (2012) Internal boundary layer model for the evolution of desert dune fields. Nat Geosci 5:206–209Google Scholar
  39. Jimenez J (2004) Turbulent flow over rough wall. Annu Rev Fluid Mech 36:173Google Scholar
  40. Khosronejad A, Sotiropoulos F (2014) Numerical simulation of sand waves in a turbulent open channel flow. J Fluid Mech 753:150–216Google Scholar
  41. Khosronejad A, Sotiropoulos F (2017) On the genesis and evolution of barchan dunes: morphodynamics. J Fluid Mech 815:117–148Google Scholar
  42. Kocurek G, Carr M, Ewing R, Havholm K, Nagar Y, Singhvi A (2007) White sands dune field, New Mexico: age, dune dynamics and recent accumulations. Sedime Geol 197:313–331Google Scholar
  43. Kok J, Parteli E, Michaels T, Karam D (2012) The physics of wind-blown sand and dust. Rep Prog Phys 75:106,901:1–72Google Scholar
  44. Li Q, Bou-Zeid E, Anderson W (2016) The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport. J Comput Phys 310:237–251Google Scholar
  45. Livingstone I, Wiggs G, Weaver C (2006) Geomorphology of desert sand dunes: a review of recent progress. Earth-Sci Rev 80:239–257Google Scholar
  46. Macdonald R, Griffiths R, Hall D (1998) An improved method for the estimation of surface roughness of obstacle arrays. Atmos Environ 32(11):1857–1864Google Scholar
  47. Martin R, Kok J (2017) Wind-invariant saltation heights imply linear scaling of aeolian saltation flux with shear stress. Sci Adv 3:e1602569–1–9Google Scholar
  48. Mejia-Alvarez R, Christensen K (2010) Low-order representations of irregular surface roughness and their impact on a turbulent boundary layer. Phys Fluids 22(015):106Google Scholar
  49. Meneveau C, Katz J (2000) Scale-invariance and turbulence models for large-eddy simulation. Annu Rev Fluid Mech 32:1–32Google Scholar
  50. Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261Google Scholar
  51. Narteau C, Zhang D, Rozier O, Claudin P (2009) Setting the length and time scales of a cellular automaton dune model from the analysis of superimposed bed forms. J Geophys Res-Earth Surf 114:F03006–1—18Google Scholar
  52. Omidyeganeh M, Piomelli U (2011) Large-eddy simulation of two-dimensional dunes in a steady, unidirectional flow. J Turbul 12:N42Google Scholar
  53. Omidyeganeh M, Piomelli U (2013a) Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. part 1. Turbulence statistics. J Fluid Mech 721:454–483Google Scholar
  54. Omidyeganeh M, Piomelli U (2013b) Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. part 2. Flow structures. J Fluid Mech 734:509–534Google Scholar
  55. Omidyeganeh M, Piomelli U, Christensen K, Best J (2013) Large eddy simulation of interacting barchan dunes in a steady, unidirectional flow. J Geophys Res-Earth Surf 118(4):2089–2104Google Scholar
  56. Ortiz P, Smolarkiewicz PK (2009) Coupling the dynamics of boundary layers and evolutionary dunes. Phys Rev E 79(041):307Google Scholar
  57. Palmer J, Mejia-Alvarez R, Best J, Christensen K (2012a) Particle-image velocimetry measurements of flow over interacting barchan dunes. Exp Fluids 52:809–829Google Scholar
  58. Palmer JA, Mejia-Alvarez R, Best JL, Christensen KT (2012b) Particle-image velocimetry measurements of flow over interacting barchan dunes. Exp Fluids 52(3):809–829Google Scholar
  59. Pan Y, Chamecki M (2016) A scaling law for the shear-production range of second-order structure functions. J Fluid Mech 801:459–474Google Scholar
  60. Piomelli U, Balaras E (2002) Wall-layer models for large-eddy simulation. Annu Rev Fluid Mech 34:349–374Google Scholar
  61. Pope S (2000) Turbulent flows. Cambridge University Press, CambridgeGoogle Scholar
  62. Porté-Agel F, Meneveau C, Parlange M (2000) A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J Fluid Mech 415:261–284Google Scholar
  63. Raupach M, Antonia R, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44:1–25Google Scholar
  64. Raupach M, Finnigan J, Brunet Y (1996a) Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol 78:351–382Google Scholar
  65. Raupach M, Finnigan J, Brunet Y (1996b) Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Boundary-Layer Meteorol 78:351–382Google Scholar
  66. Shao Y (2008) Physics and modelling of wind erosion. Springer, BerlinGoogle Scholar
  67. Smith AB, Jackson DW, Cooper JAG (2017) Three-dimensional airflow and sediment transport patterns over barchan dunes. Geomorphology 278:28–42Google Scholar
  68. Stevens R, Meneveau C (2017) Flow structure and turbulence in wind farms. Annu Rev Fluid Mech 49:311–339Google Scholar
  69. Stoesser T, Braun C, Garcia-Villalba M, Rodi W (2008) Turbulence structures in flow over two-dimensional dunes. J Hydraul Eng 134(1):42–55Google Scholar
  70. Townsend A (1976) The structure of turbulent shear flow. Cambridge University Press, CambridgeGoogle Scholar
  71. Tseng YH, Meneveau C, Parlange M (2006) Modeling flow around bluff bodies and predicting urban dispersion using large-eddy simulation. Environ Sci Technol 40:2653–2662Google Scholar
  72. Wang C, Anderson W (2018) Large-eddy simulation of turbulent flow over spanwise-offset barchan dunes: interdune vortex stretching drives asymmetric erosion. Phys Rev E 98(3):033112Google Scholar
  73. Wang C, Tang Z, Bristow N, Blois G, Christensen K, Anderson W (2016) Numerical and experimental study of flow over stages of an offset merger dune interaction. Comput Fluids 158:72–83Google Scholar
  74. Webb NP, Galloza MS, Zobeck TM, Herrick JE (2016) Threshold wind velocity dynamics as a driver of aeolian sediment mass flux. Aeolian Res 20:45–58Google Scholar
  75. Werner B (1995) Eolian dunes: computer simulations and attractor interpretation. Geology 23:1107–1110Google Scholar
  76. Xie ZT, Coceal O, Castro I (2008) Large-eddy simulation of flows over random urban-like obstacles. Boundary-Layer Meteorol 129:1–23Google Scholar
  77. Zgheib N, Fedele J, Hoyal D, Perillo M, Balachandar S (2018a) Direct numerical simulation of transverse ripples: 1. Pattern initiation and bedform interactions. J Geophys Res-Earth Surf 123:448–477Google Scholar
  78. Zgheib N, Fedele J, Hoyal D, Perillo M, Balachandar S (2018b) Direct numerical simulation of transverse ripples: 2. Self-similarity, bedform coarsening, and effect of neighboring structures. J Geophys Res-Earth Surf 123:478–500Google Scholar
  79. Zhu X, Anderson W (2018) Turbulent flow over urban-like fractals: prognostic roughness model for unresolved generations. J Turbul 19:995–1016Google Scholar
  80. Zhu X, Iungo G, Leonardi S, Anderson W (2017) Parametric study of urban-like topographic statistical moments relevant to a priori modelling of bulk aerodynamic parameters. Boundary-Layer Meteorol 162:231–253Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentThe University of Texas at DallasRichardsonUSA

Personalised recommendations