Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-10-30T03:19:27.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle boundary layer above and downstream of an area source: scaling, simulations, and pollen transport

Published online by Cambridge University Press:  02 August 2011

Marcelo Chamecki  and
Charles Meneveau
Marcelo Chamecki*
Affiliation:
Department of Meteorology, Pennsylvania State University, University Park, PA 16802, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: chamecki@meteo.psu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Dispersion of small particles emitted from an area source at the surface into a fully developed high-Reynolds-number boundary layer flow is studied as a theoretical model for pollen dispersion in the neutral atmospheric boundary layer. The particle plume above the area source is assumed to behave as a particle concentration boundary layer. Boundary layer scaling and the assumption of self-preservation lead to an analytical solution in the form of a similarity function that has an additional dependence on the ratio of gravitational settling and turbulent diffusion velocities. Similar arguments are used to predict patterns of deposition onto the surface downstream of the source. Theoretical predictions are tested using a suite of large-eddy-simulation numerical experiments, with good agreement. The combined analysis of theoretical and numerical results reveals interesting features in the patterns of downstream deposition, such as non-monotonic trends in isolation distance with particle settling velocity and surprisingly large isolation distances for practically relevant parameter ranges. Possible effects of turbulence on effective settling velocity are highlighted.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulent boundary layers

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 683 , 25 September 2011 , pp. 1 - 26
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Ahmed, A. M. & Elghobashi, S. 2000 On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles. Phys. Fluids 12, 1–25.CrossRefGoogle Scholar
2. Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77–105.CrossRefGoogle Scholar
3. Arritt, R. W., Clark, C. A., Goggi, A. S., Sanchez, H. L., Westgate, M. E. & Riese, J. M. 2007 Lagrangian numerical simulations of canopy air flow effects on maize pollen dispersal. Field Crops Res. 102, 151–162.CrossRefGoogle Scholar
4. Aylor, D. E. 2002 Settling speed of corn (Zea mays) pollen. J. Aerosol Sci. 33, 1601–1607.CrossRefGoogle Scholar
5. Berrouk, A. S., Laurence, D., Riley, J. J. & Stock, D. E. 2006 Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow. J. Turbul. 8, 1–20.Google Scholar
6. Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2004 Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour. Res. 40 (2), W02505.CrossRefGoogle Scholar
7. Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.CrossRefGoogle Scholar
8. Bouvet, T. & Wilson, J. D. 2006 An approximate analytical solution for the deposition of heavy particles released from an elevated line source. Boundary-Layer Meteorol. 119, 1–18.CrossRefGoogle Scholar
9. Brooke, J. W., Kontomaris, K., Hanratty, T. J. & McLaughlin, J. B. 1992 Turbulent deposition and trapping of aerosols at a wall. Phys. Fluids A 4, 825–834.CrossRefGoogle Scholar
10. Brutsaert, W. 1982 Evaporation into the Atmosphere. Reidel.CrossRefGoogle Scholar
11. Calder, K. L. 1949 Eddy diffusion and evaporation in flow over aerodynamically smooth and rough surfaces: a treatment based on laboratory laws of turbulent flow with special reference to conditions in the lower atmosphere. Q. J. Mech. Appl. Math. 2, 153–176.CrossRefGoogle Scholar
12. Chamberlain, A. C. 1967 Transport of Lycopodium spores and other small particles to rough surfaces. Proc. R. Soc. Lond. A 296, 45–70.Google Scholar
13. Chamecki, M., van Hout, R., Meneveau, C. & Parlange, M. B. 2007 Concentration profiles of particles settling in the neutral and stratified atmospheric boundary layer. Boundary-Layer Meteorol. 125 (1), 25–38.CrossRefGoogle Scholar
14. Chamecki, M., Meneveau, C. & Parlange, M. B. 2008 A hybrid spectral/finite-volume algorithm for large-eddy simulation of scalars in the atmospheric boundary layer. Boundary-Layer Meteorol. 128 (3), 473–484.CrossRefGoogle Scholar
15. Chamecki, M., Meneveau, C. & Parlange, M. B. 2009 Large eddy simulation of pollen transport in the atmospheric boundary layer. J. Aerosol Sci. 40 (3), 241–255.CrossRefGoogle Scholar
16. Chou, Y.-J. & Fringer, O. B. 2008 Modeling dilute sediment suspension using large-eddy simulation with a dynamic mixed model. Phys. Fluids 20, 115103.CrossRefGoogle Scholar
17. Coleman, S. W. & Vassilicos, J. C. 2009 A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence. Phys. Fluids 21, 113301.CrossRefGoogle Scholar
18. Dupont, S., Brunet, Y. & Jarosz, N. 2006 Eulerian modelling of pollen dispersal over heterogeneous vegetation canopies. Agric. Forest Meteorol. 141, 82–104.CrossRefGoogle Scholar
19. Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52, 309–329.CrossRefGoogle Scholar
20. Frost, R. 1946 Turbulence and diffusion in the lower atmosphere. Proc. R. Soc. Lond. A 186, 20–35.Google Scholar
21. Garratt, J. R. 1994 The Atmospheric Boundary Layer. Cambridge University Press.Google Scholar
22. Gaskell, P. H. & Lau, A. K. C. 1988 Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm. Intl J. Numer. Meth. Fluids 8, 617–641.CrossRefGoogle Scholar
23. Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
24. Godson, W. L. 1957 The diffusion of particulate matter from an elevated source. Archiv für Meteorologie, Geophysik und Bioklimatologie A 10, 305–327.CrossRefGoogle Scholar
25. Gregory, P. H. 1973 Microbiology of the Atmosphere, 2nd edn. Wiley.Google Scholar
26. Hartel, C., Meiburg, E. & Necker, F. 2000 Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418, 189–212.CrossRefGoogle Scholar
27. Honnay, O., Jacquemyn, H., Bossuyt, B. & Hermy, M. 2005 Forest fragmentation effects on patch occupancy and population viability of herbaceous plant species. New Phytol. 166 (3), 723–736.CrossRefGoogle ScholarPubMed
28. van Hout, R., Chamecki, M., Brush, G., Katz, J. & Parlange, M. B. 2008 The influence of local meteorological conditions on the circadian rhythm of corn (Zea mays L.) pollen emission. Agric. Forest Meteorol. 148, 1078–1092.CrossRefGoogle Scholar
29. Jarosz, N., Loubet, B., Durand, B., McCartney, A., Foueillassar, X. & Huber, L. 2003 Field measurements of airborne concentration and deposition rate of maize pollen. Agric. Forest Meteorol. 119, 37–51.CrossRefGoogle Scholar
30. Jarosz, N., Loubet, B. & Huber, L. 2004 Modelling airborne concentration and deposition rate of maize pollen. Atmos. Environ. 38, 5555–5566.CrossRefGoogle Scholar
31. Kader, B. A. & Yaglom, A. M. 1972 Heat and mass transfer laws for fully turbulent wall flows. Intl J. Heat Mass Transfer 15, 2329–2351.CrossRefGoogle Scholar
32. Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 Particle behaviour in the turbulent boundary layer. Part I. Motion, deposition, and entrainment. Phys. Fluids 7, 1107–1121.CrossRefGoogle Scholar
33. Kaimal, J. C. & Finnigan, J. J. 1994 Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press.CrossRefGoogle Scholar
34. Kiger, K. T. & Lasheras, J. C. 1997 Dissipation due to particle/turbulence interaction in a two-phase, turbulent, shear layer. Phys. Fluids 3005, 1–19.Google Scholar
35. Kind, R. J. 1992 One-dimensional aeolian suspension above beds of loose particles: a new concentration-profile equation. Atmos. Environ. A 26 (5), 927–931.CrossRefGoogle Scholar
36. Klein, E. K., Lavigne, C., Foueillassar, X., Gouyon, P. H. & Larédo, C. 2003 Corn pollen dispersal: quasi-mechanistic models and field experiments. Ecol. Monogr. 73, 131–150.CrossRefGoogle Scholar
37. Lagarias, J. C., Reeds, J. A., Wright, M. H. & Wright, P. E. 1998 Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J. Optim. 9 (1), 112–147.CrossRefGoogle Scholar
38. Lehning, M., Löwe, H., Ryser, M. & Raderschall, N. 2008 Inhomogeneous precipitation distribution and snow transport in steep terrain. Water Resour. Res. 44, W07404.CrossRefGoogle Scholar
39. Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315.CrossRefGoogle Scholar
40. Martin, M., Chamecki, M. & Brush, G. S. 2010 Anthesis synchronization and floral morphology determine diurnal patterns of ragweed pollen dispersal. Agric. Forest Meteorol. 150, 1307–1317.CrossRefGoogle Scholar
41. Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
42. Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
43. McCartney, H. A. & Lacey, M. E. 1991 Wind dispersal of pollen from crops of oilseed rape (Brassica napus L.). J. Aerosol Sci. 22 (4), 467–477.CrossRefGoogle Scholar
44. McLaughlin, J. B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1, 1210–1224.CrossRefGoogle Scholar
45. Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
46. Messeguer, J. 2003 Gene flow assessment in transgenic plants. Plant Cell, Tissue and Organ Culture 73, 201–212.CrossRefGoogle Scholar
47. Necker, F., Haertel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow 28, 279–300.CrossRefGoogle Scholar
48. Necker, F., Haertel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.CrossRefGoogle Scholar
49. O’Connell, L. M., Mosseler, A. & Rajora, O. P. 2007 Extensive long-distance pollen dispersal in a fragmented landscape maintains genetic diversity in white spruce. J. Heredity 98, 640–645.CrossRefGoogle Scholar
50. Pedinotti, S., Mariotti, G. & Banerjee, S. 1992 Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels. Intl J. Multiphase Flow 18, 927–941.CrossRefGoogle Scholar
51. Philip, J. R. 1959 The theory of local advection. Part I. J. Atmos. Sci. 16, 535–547.Google Scholar
52. Prandtl, L. 1952 Essentials of Fluid Dynamics. Blackie.Google Scholar
53. Ramsay, G. 2005 Pollen dispersal vectored by wind or insects. In Gene Flow from GM Plants (ed. Poppy, G. M. & Wilkinson, M. J. ), chap. 5, pp. 43–73. Blackwell.CrossRefGoogle Scholar
54. Rashidi, M., Hetsroni, G. & Banerjee, S. 1990 Particle-turbulence interaction in a boundary layer. Intl J. Multiphase Flow 16, 935–949.CrossRefGoogle Scholar
55. Raynor, G. S., Ogden, E. C. & Hayes, J. V. 1972a Dispersion and deposition of timothy pollen from experimental sources. Agric. Meteorol. 9, 347–366.CrossRefGoogle Scholar
56. Raynor, G. S., Ogden, E. C. & Hayes, J. V. 1970 Dispersion and deposition of ragweed pollen from experimental sources. J. Appl. Meteorol. 9 (6), 885–895.2.0.CO;2>CrossRefGoogle Scholar
57. Raynor, G. S., Ogden, E. C. & Hayes, J. V. 1972b Dispersion and deposition of corn pollen from experimental sources. Agronomy J. 64, 420–427.CrossRefGoogle Scholar
58. Reeks, M. W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aerosol Sci. 14, 729–739.CrossRefGoogle Scholar
59. Rounds, W. 1955 Solutions of the two-dimensional diffusion equations. Trans. Am. Geophys. U. 36, 395–405.Google Scholar
60. Rouse, H. 1937 Modern conceptions of the mechanics of fluid turbulence. Trans. ASCE 102, 463–505.Google Scholar
61. Rouson, D. W. I. & Eaton, J. K. 2001 On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech. 428, 149–169.CrossRefGoogle Scholar
62. Shaw, M. W., Harwood, T. D., Wilkinson, M. J. & Elliott, L. 2006 Assembling spatially explicit landscape models of pollen and spore dispersal by wind for risk assessment. Proc. R. Soc. Lond. B 273, 1705–1713.Google ScholarPubMed
63. Shotorban, B. & Balachandar, S. 2007 A Eulerian model for large-eddy simulation of concentration particles with small Stokes numbers. Phys. Fluids 19, 118107.CrossRefGoogle Scholar
64. Smith, D. M. 2001 Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions. ACM Trans. Math. Softw. 27, 377–387.CrossRefGoogle Scholar
65. Snyder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity autocorrection functions in a turbulent flow. J. Fluid Mech. 48, 41–47.CrossRefGoogle Scholar
66. Sork, V. L. & Smouse, P. E. 2006 Genetic analysis of landscape connectivity in tree populations. Landscape Ecol. 21, 821–836.CrossRefGoogle Scholar
67. Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3, 1169–1178.CrossRefGoogle Scholar
68. Sutton, O. G. 1934 Wind structure and evaporation in a turbulent atmosphere. Proc. R. Soc. Lond. A 146, 701–722.Google Scholar
69. Timmons, A. M., O’Brien, E. T., Charters, Y. M., Dubbels, S. J. & Wilkinson, M. J. 1995 Assessing the risks of wind pollination from fields of genetically modified Brassica napus ssp. oleifera . Euphytica 85, 417–423.CrossRefGoogle Scholar
70. Vinkovic, I., Aguirre, C., Simoens, S. & Gorokhovski, M. 2006 Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow. Intl J. Multiphase Flow 32, 344–364.CrossRefGoogle Scholar
71. Walklate, P. J., Hunt, J. C. R., Higson, H. L. & Sweet, J. B. 2004 A model of pollen-mediated gene flow for oilseed rape. Proc. R. Soc. Lond. B 271, 441–449.CrossRefGoogle Scholar
72. Wang, L. P. & Maxey, M. R. 1993 Settling velocity and concentration of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
73. Yeh, G.-T. & Brutsaert, W. 1970 Perturbation solution of an equation of atmospheric turbulent diffusion. J. Geophys. Res. 75, 5173–5178.CrossRefGoogle Scholar
74. Zedler, E. A. & Street, R. L. 2001 Large-eddy simulation of sediment transport: currents over ripples. J. Hydraul. Engng 127 (6), 444–452.CrossRefGoogle Scholar