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Boundary-Layer Meteorology

, Volume 128, Issue 2, pp 205–228 | Cite as

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

  • Nikki Vercauteren
  • Elie Bou-Zeid
  • Marc B. Parlange
  • Ulrich Lemmin
  • Hendrik Huwald
  • John Selker
  • Charles Meneveau
Original Paper

Abstract

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.

Keywords

Large-eddy simulation Non-linear model Smagorinsky model Turbulent Prandtl number Turbulent Schmidt number 

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References

  1. Albertson JD, Parlange MB (1999a) Surface length scales and shear stress: Implications for land-atmosphere interaction over complex terrain. Water Resour Res 35: 2121–2132. doi: 10.1029/1999WR900094 CrossRefGoogle Scholar
  2. Albertson JD, Parlange MB (1999b) Natural integration of scalar fluxes from complex terrain. Adv Water Resour 23: 239–252. doi: 10.1016/S0309-1708(99)00011-1 CrossRefGoogle Scholar
  3. Assouline S, Tyler SW, Tanny J, Cohen S, Bou-Zeid E, Parlange MB et al (2008) Evaporation from three water bodies of different sizes and climates: measurements and scaling analysis. Adv Water Resour 31: 160–172. doi: . doi:10.1016/j.advwatres.2007.07.003 CrossRefGoogle Scholar
  4. Bardina J, Ferziger JH, Reynolds WC (1980) Improved subgrid scale models for large eddy simulation. American Institute of Aeronautics and Astronautics Pap 80–1357Google Scholar
  5. 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: W02505. doi: 10.1029/2003WR002475 CrossRefGoogle Scholar
  6. Bou-Zeid E, Meneveau C, Parlange MB (2005) A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys Fluids 17: 025105. doi: 10.1063/1.1839152 CrossRefGoogle Scholar
  7. Bou-Zeid E, Parlange MB, Meneveau C (2007) On the parameterization of surface roughness at regional scales. J Atmos Sci 64: 216–227. doi: 10.1175/JAS3826.1 CrossRefGoogle Scholar
  8. Bradbrook KF, Lane SN, Richards KS, Biron PM, Roy AG (2000) Large eddy simulation of periodic flow characteristics at river channel confluences. J Hydraul Res 38: 207–215Google Scholar
  9. Brocchini M, Peregrine DH (2001a) The dynamics of strong turbulence at free surfaces. Part 1. Description. J Fluid Mech 449: 225–254. doi: 10.1017/S0022112001006012 CrossRefGoogle Scholar
  10. Brocchini M, Peregrine DH (2001b) The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions. J Fluid Mech 449: 255–290. doi: 10.1017/S0022112001006024 CrossRefGoogle Scholar
  11. Brown AR, Derbyshire SH, Mason PJ (1994) Large-eddy simulation of stable atmospheric boundary-layers with a revised stochastic subgrid model. Q J R Meteorol Soc 120: 1485–1512. doi: 10.1002/qj.49712052004 CrossRefGoogle Scholar
  12. Brutsaert W (1982) Evaporation into the atmosphere: theory, history, and applications. Reidel, Dordrecht, Holland, p 299Google Scholar
  13. Brutsaert W (1998) Land-surface water vapor and sensible heat flux: spatial variability, homogeneity, and measurement scales. Water Resour Res 34: 2433–2442. doi: 10.1029/98WR01340 CrossRefGoogle Scholar
  14. Chamecki M, Meneveau C, Parlange MB (2007) The local structure of atmospheric turbulence and its effect on the Smagorinsky model for large eddy simulation. J Atmos Sci 64: 1941–1958. doi: 10.1175/JAS3930.1 CrossRefGoogle Scholar
  15. Clark RA, Ferziger JH, Reynolds WC (1979) Evaluation of sub-grid-scale models using an accurately simulated turbulent-flow. J Fluid Mech 91: 1–16. doi: 10.1017/S002211207900001X CrossRefGoogle Scholar
  16. DeCosmo J, Katsaros KB, Smith SD, Anderson RJ, Oost WA, Bumke K et al (1996) Air-sea exchange of water vapor and sensible heat: the humidity exchange over the sea (HEXOS) results. J Geophys Res-Oceans 101: 12001–12016. doi: 10.1029/95JC03796 CrossRefGoogle Scholar
  17. Edson J, Crawford T, Crescenti J, Farrar T, Frew N, Gerbi G et al (2007) The coupled boundary layers and air-sea transfer experiment in low winds. Bull Amer Meteorol Soc 88: 341–356. doi: 10.1175/BAMS-88-3-341 CrossRefGoogle Scholar
  18. Germano M, Piomelli U, Moin P, Cabot WH (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3: 1760–1765. doi: 10.1063/1.857955 CrossRefGoogle Scholar
  19. Higgins CW, Parlange MB, Meneveau C (2003) Alignment trends of velocity gradients and subgrid-scale fluxes in the turbulent atmospheric boundary layer. Boundary-Layer Meteorol 109: 59–83. doi: 10.1023/A:1025484500899 CrossRefGoogle Scholar
  20. Higgins CW, Meneveau C, Parlange MB (2007) The effect of filter dimension on the subgrid-scale stress, heat flux, and tensor alignments in the atmospheric surface layer. J Atmos Ocean Technol 24: 360–375. doi: 10.1175/JTECH1991.1 CrossRefGoogle Scholar
  21. Katul GG, Parlange MB (1995) Analysis of land-surface heat fluxes using the orthonormal wavelet approach. Water Resour Res 31: 2743–2749. doi: 10.1029/95WR00003 CrossRefGoogle Scholar
  22. Kays WM (1994) Turbulent Prandtl number – Where are we? J Heat Transfer 116: 284–295. doi: 10.1115/1.2911398 CrossRefGoogle Scholar
  23. Keylock CJ, Hardy RJ, Parsons DR, Ferguson RI, Lane SN, Richards KS (2005) The theoretical foundations and potential for large-eddy simulation (LES) in fluvial geomorphic and sedimentological research. Earth Sci Rev 71: 271–304. doi: 10.1016/j.earscirev.2005.03.001 CrossRefGoogle Scholar
  24. Kleissl J, Meneveau C, Parlange MB (2003) On the magnitude and variability of subgrid-scale eddy-diffusion coefficients in the atmospheric surface layer. J Atmos Sci 60: 2372–2388. doi :10.1175/1520-0469(2003)060<2372:OTMAVO>2.0.CO;2CrossRefGoogle Scholar
  25. Kleissl J, Parlange MB, Meneveau C (2004) Field experimental study of dynamic Smagorinsky models in the atmospheric surface layer. J Atmos Sci 61: 2296–2307. doi :10.1175/1520-0469(2004)061<2296: FESODS>2.0.CO;2CrossRefGoogle Scholar
  26. Lilly DK (1967) The representation of small scale turbulence in numerical simulation experiments. In: IBM Scientific computing symposium on environmental sciences, White Plains, New York, pp 195–209Google Scholar
  27. Liu SW, Meneveau C, Katz J (1994) On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J Fluid Mech 275: 83–119. doi: 10.1017/S0022112094002296 CrossRefGoogle Scholar
  28. Mason PJ (1989) Large-eddy simulation of the convective atmospheric boundary-layer. J Atmos Sci 46: 1492–1516. doi :10.1175/1520-0469(1989)046<1492:LESOTC>2.0.CO;2CrossRefGoogle Scholar
  29. Mason PJ, Brown AR (1999) On subgrid models and filter operations in large eddy simulations. J Atmos Sci 56: 2101–2114. doi :10.1175/1520-0469(1999)056<2101:OSMAFO>2.0.CO;2CrossRefGoogle Scholar
  30. Mason PJ, Thomson DJ (1992) Stochastic backscatter in large-eddy simulations of boundary-layers. J Fluid Mech 242: 51–78. doi: 10.1017/S0022112092002271 CrossRefGoogle Scholar
  31. Meneveau C (1994) Statistics of turbulence subgrid-scale stresses – necessary conditions and experimental tests. Phys Fluids 6: 815–833. doi: 10.1063/1.868320 CrossRefGoogle Scholar
  32. Meneveau C, Katz J (2000) Scale-invariance and turbulence models for large-eddy simulation. Annu Rev Fluid Mech 32: 1–32. doi: 10.1146/annurev.fluid.32.1.1 CrossRefGoogle Scholar
  33. Mitsuishi A, Hasegawa Y, Kasagi N (2003): Large eddy simulation of mass transfer across an air-water interface at high schmidt numbers. In: The 6th ASME-JSME thermal engineering joint conference, Hawai, USA, paper number TED-AJ03-231.Google Scholar
  34. Moeng CH (1984) A large-eddy-simulation model for the study of planetary boundary-layer turbulence.. J Atmos Sci 41: 2052–2062. doi :10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;2CrossRefGoogle Scholar
  35. Moin P, Squires K, Cabot W, Lee S (1991) A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys Fluids A 3: 2746–2757. doi: 10.1063/1.858164 CrossRefGoogle Scholar
  36. O’Sullivan PL, Biringen S, Huser A (2001) A priori evaluation of dynamic subgrid models of turbulence in square duct flow. J Eng Math 40: 91–108. doi: 10.1023/A:1017552106889 CrossRefGoogle Scholar
  37. Parlange MB, Eichinger WE, Albertson JD (1995) Regional-scale evaporation and the atmospheric boundary-layer. Rev Geophys 33: 99–124. doi: 10.1029/94RG03112 CrossRefGoogle Scholar
  38. Patton EG, Sullivan PP, Moeng CH (2005) The influence of idealized heterogeneity on wet and dry planetary boundary layers coupled to the land surface. J Atmos Sci 62: 2078–2097. doi: 10.1175/JAS3465.1 CrossRefGoogle Scholar
  39. Piomelli U (1999) Large-eddy simulation: achievements and challenges. Prog Aerosp Sci 35: 335–362. doi: 10.1016/S0376-0421(98)00014-1 CrossRefGoogle Scholar
  40. Pitsch H, Steiner H (2000) Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D). Phys Fluids 12: 2541–2554. doi: 10.1063/1.1288493 CrossRefGoogle Scholar
  41. Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge, UK, p 771Google Scholar
  42. Pope SB (2004) Ten questions concerning the large-eddy simulation of turbulent flows. N J Phys 6: 771. doi: 10.1088/1367-2630/6/1/035 CrossRefGoogle Scholar
  43. Porte-Agel F (2004) A scale-dependent dynamic model for scalar transport in large-eddy simulations of the atmospheric boundary layer. Boundary-Layer Meteorol 112: 81–105. doi: 10.1023/B:BOUN.0000020353.03398.20 CrossRefGoogle Scholar
  44. Porte-Agel F, Meneveau C, Parlange MB (1998) Some basic properties of the surrogate subgrid-scale heat flux in the atmospheric boundary layer. Boundary-Layer Meteorol 88: 425–444. doi: 10.1023/A:1001521504466 CrossRefGoogle Scholar
  45. Porte-Agel F, Parlange MB, Meneveau C, Eichinger WE, Pahlow M (2000) Subgrid-scale dissipation in the atmospheric surface layer: Effects of stability and filter dimension. J Hydromet 1: 75–87. doi :10.1175/1525-7541(2000)001<0075:SSDITA>2.0.CO;2CrossRefGoogle Scholar
  46. Porte-Agel F, Pahlow M, Meneveau C, Parlange MB (2001a) Atmospheric stability effect on subgrid- scale physics for large-eddy simulation. Adv Water Resour 24: 1085–1102. doi: 10.1016/S0309-1708(01)00039-2 CrossRefGoogle Scholar
  47. Porte-Agel F, Parlange MB, Meneveau C, Eichinger WE (2001) A priori field study of the subgrid-scale heat fluxes and dissipation in the atmospheric surface layer. J Atmos Sci 58: 2673–2698. doi :10.1175/1520-0469(2001)058<2673:APFSOT>2.0.CO;2CrossRefGoogle Scholar
  48. Sagaut P (2003) Large eddy simulation for incompressible flows. Springer-Verlag, Berlin, p 426Google Scholar
  49. Scotti A, Meneveau C, Lilly DK (1993) Generalized Smagorinsky model for anisotropic grids. Phys Fluids A 5: 2306–2308. doi: 10.1063/1.858537 CrossRefGoogle Scholar
  50. Shen L, Yue DKP (2001) Large-eddy simulation of free-surface turbulence. J Fluid Mech 440: 75–116. doi: 10.1017/S0022112001004669 CrossRefGoogle Scholar
  51. Smagorinsky J (1963) General circulation experiments with the primitive equations: I The basic experiment. Mon Weather Rev 91: 99–164. doi :10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2CrossRefGoogle Scholar
  52. Stoll R, Porte-Agel F (2006) Dynamic subgrid-scale models for momentum and scalar fluxes in large-eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resour Res 42: W01409. doi: 10.1029/2005WR003989 CrossRefGoogle Scholar
  53. Sullivan PP, McWilliams JC, Moeng CH (2000) Simulation of turbulent flow over idealized water waves. J Fluid Mech 404: 47–85. doi: 10.1017/S0022112099006965 CrossRefGoogle Scholar
  54. Sullivan PP, Horst TW, Lenschow DH, Moeng CH, Weil JC (2003) Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling. J Fluid Mech 482: 101–139. doi: 10.1017/S0022112003004099 CrossRefGoogle Scholar
  55. Sullivan PP, Edson JB, Horst TW, Wyngaard JC, Kelly M (2006) Subfilter scale fluxes in the marine surface layer: results from the ocean horizontal array turbulence study (OHATS). In: 17th Symposium on boundary layers and turbulence, San Diego, U.S.A.Google Scholar
  56. Sullivan PP, Mcwilliams JC, Melville WK (2007) Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers. J Fluid Mech 593: 405–452. doi: 10.1017/S002211200700897X CrossRefGoogle Scholar
  57. Tao B, Katz J, Meneveau C (2002) Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J Fluid Mech 457: 35–78. doi: 10.1017/S0022112001007443 CrossRefGoogle Scholar
  58. Tong CN, Wyngaard JC, Brasseur JG (1999) Experimental study of the subgrid-scale stresses in the atmospheric surface layer. J Atmos Sci 56: 2277–2292. doi :10.1175/1520-0469(1999)056<2277:ESOTSS>2.0.CO;2CrossRefGoogle Scholar
  59. Webb EK, Pearman GI, Leuning R (1980) Correction of flux measurements for density effects due to heat and water-vapor transfer. Quart J Roy Meteorol Soc 106: 85–100. doi: 10.1002/qj.49710644707 CrossRefGoogle Scholar
  60. Wood N (2000) Wind flow over complex terrain: a historical perspective and the prospect for large-eddy modelling. Boundary-Layer Meteorol 96: 11–32. doi: 10.1023/A:1002017732694 CrossRefGoogle Scholar
  61. Yimer I, Campbell I, Jiang LY (2002) Estimation of the turbulent Schmidt number from experimental profiles of axial velocity and concentration for high-Reynolds-number jet flows. Can Aeronaut Space J 48: 195–200Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Nikki Vercauteren
    • 1
  • Elie Bou-Zeid
    • 1
    • 2
  • Marc B. Parlange
    • 1
  • Ulrich Lemmin
    • 1
  • Hendrik Huwald
    • 1
  • John Selker
    • 3
  • Charles Meneveau
    • 4
  1. 1.School of Architecture, Civil and Environmental EngineeringÉcole Polytechnique Fédérale de Lausanne-EPFLLausanneSwitzerland
  2. 2.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA
  3. 3.Department of Biological and Ecological EngineeringOregon State UniversityCorvallisUSA
  4. 4.Department of Mechanical Engineering and Center for Environmental and Applied Fluid MechanicsThe Johns Hopkins UniversityBaltimoreUSA

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