Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-01T10:18:37.444Z Has data issue: false hasContentIssue false
  • English
  • Français

Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier

Published online by Cambridge University Press:  10 November 2010

ELIE BOU-ZEID ,
CHAD HIGGINS ,
HENDRIK HUWALD ,
CHARLES MENEVEAU  and
MARC B. PARLANGE
ELIE BOU-ZEID*
Affiliation:
Department of Civil and Environmental Engineering, Princeton University, E414 EQuad, Princeton, NJ 08544, USA
CHAD HIGGINS
Affiliation:
School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne-EPFL, Lausanne, Switzerland
HENDRIK HUWALD
Affiliation:
School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne-EPFL, Lausanne, Switzerland
CHARLES MENEVEAU
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218-2680, USA
MARC B. PARLANGE
Affiliation:
School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne-EPFL, Lausanne, Switzerland
*
†Email address for correspondence: ebouzeid@princeton.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A field experiment – the Snow Horizontal Array Turbulence Study (SnoHATS) – has been performed over an extensive glacier in Switzerland in order to study small-scale turbulence in the stable atmospheric surface layer, and to investigate the role, dynamics and modelling of the subgrid scales (SGSs) in the context of large-eddy simulations. The a priori data analysis aims at comparing the role and behaviour of the SGSs under stable conditions with previous studies under neutral or unstable conditions. It is found that the SGSs in a stable surface layer remain an important sink of temperature variance and turbulent kinetic energy from the resolved scales and carry a significant portion of the fluxes when the filter scale is larger than the distance to the wall. The fraction of SGS fluxes (out of the total fluxes) is found to be independent of stability. In addition, the stress–strain alignment is similar to the alignment under neutral and unstable conditions. The model coefficients vary considerably with stability but in a manner consistent with previous findings, which also showed that scale-dependent dynamic models can capture this variation. Furthermore, the variation of the coefficients for both momentum and heat SGS fluxes can be shown to be better explained by stability parameters based on vertical gradients, rather than vertical fluxes. These findings suggest that small-scale turbulence dynamics and SGS modelling under stable conditions share many important properties with neutral and convective conditions, and that a unified approach is thus possible. This paper concludes with a discussion of some other challenges for stable boundary-layer simulations that are not encountered in the neutral or unstable cases.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 480 - 515
Copyright
Copyright © Cambridge University Press 2010

References

REFERENCES

Aluie, H. & Eyink, G. L. 2009 Localness of energy cascade in hydrodynamic turbulence. Part II. Sharp spectral filter. Phys. Fluids 21 (11), 115108.CrossRefGoogle Scholar
Armenio, V. & Sarkar, S. 2002 An investigation of stably stratified turbulent channel flow using large-eddy simulation. J. Fluid Mech. 459, 1–42.CrossRefGoogle Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30 (8), 2343–2353.CrossRefGoogle Scholar
Basu, S., Holtslag, A. A. M., Van De Wiel, B. J. H., Moene, A. F. & Steeneveld, G. J. 2008 An inconvenient ‘truth’ about using sensible heat flux as a surface boundary condition in models under stably stratified regimes. Acta Geophys. 56 (1), 88–99.CrossRefGoogle Scholar
Basu, S., Porte-Agel, F., Foufoula-Georgiou, E., Vinuesa, J. F. & Pahlow, M. 2006 Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: an integration of field and laboratory measurements with large-eddy simulations. Boundary-Layer Meteorol. 119 (3), 473–500.CrossRefGoogle Scholar
Beare, R. J. & Macvean, M. K. 2004 Resolution sensitivity and scaling of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol. 112 (2), 257–281.CrossRefGoogle Scholar
Beare, R. J., MacVean, M. K., Holtslag, A. A. M., Cuxart, J., Esau, I., Golaz, J. C., Jimenez, M. A., Khairoutdinov, M., Kosovic, B., Lewellen, D., Lund, T. S., Lundquist, J. K., McCabe, A., Moene, A. F., Noh, Y., Raasch, S. & Sullivan, P. 2006 An intercomparison of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol. 118 (2), 247–272.CrossRefGoogle Scholar
Beljaars, A. C. M. 1995 The impact of some aspects of the boundary layer scheme in the ECMWF model. In Seminar on Parametrization of Subgrid Scale Physical Processes, 5–9 September 1994 – ECMWF, Reading, UK, pp. 125–161.Google Scholar
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
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
Bou-Zeid, E., Parlange, M. B. & Meneveau, C. 2007 On the parameterization of surface roughness at regional scales. J. Atmos. Sci. 64 (1), 216–227.CrossRefGoogle Scholar
Bou-Zeid, E., Vercauteren, N., Parlange, M. B. & Meneveau, C. 2008 Scale dependence of subgrid-scale model coefficients: an a priori study. Phys. Fluids 20 (11), 115106–115106.CrossRefGoogle Scholar
Brasseur, J. G. & Wei, T. 2010 Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys. Fluids 22 (2), 021303.CrossRefGoogle Scholar
De Bruin, H. A. R. 1994 Analytic solutions of the equations governing the temperature fluctuation method. Boundary-Layer Meteorol. 68 (4), 427–432.CrossRefGoogle Scholar
Brutsaert, W. 1998 Land-surface water vapor and sensible heat flux: spatial variability, homogeneity and measurement scales. Water Resour. Res. 34 (10), 2433–2442.CrossRefGoogle Scholar
Canuto, V. M. & Minotti, F. 1993 Stratified turbulence in the atmosphere and oceans – a new subgrid model. J. Atmos. Sci. 50 (13), 1925–1935.2.0.CO;2>CrossRefGoogle Scholar
Chamecki, M. 2010 Modelling subgrid-scale heat fluxes in the neutral and stratified atmospheric boundary layer. J. Turbul. 11 (13), 1–16.CrossRefGoogle Scholar
Chamecki, M. & Dias, N. L. 2004 The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer. Q. J. R. Meteorol. Soc. 130 (603), 2733–2752.CrossRefGoogle Scholar
Chamecki, M., Meneveau, C. & Parlange, M. B. 2007 The local structure of atmospheric turbulence and its effect on the Smagorinsky model for large eddy simulation. J. Atmos. Sci. 64 (6), 1941–1958.CrossRefGoogle Scholar
Chamorro, L. P. & Porte-Agel, F. 2009 Velocity and surface shear stress distributions behind a rough-to-smooth surface transition: a simple new model. Boundary-Layer Meteorol. 130 (1), 29–41.CrossRefGoogle Scholar
Champagne, F. H., Friehe, C. A., Larue, J. C. & Wyngaard, J. C. 1977 Flux measurements, flux estimation techniques and fine-scale turbulence measurements in unstable surface layer over land. J. Atmos. Sci. 34 (3), 515–530.2.0.CO;2>CrossRefGoogle Scholar
Cheng, Y. G. & Brutsaert, W. 2005 Flux-profile relationships for wind speed and temperature in the stable atmospheric boundary layer. Boundary-Layer Meteorol. 114 (3), 519–538.CrossRefGoogle Scholar
Cheng, Y. G., Parlange, M. B. & Brutsaert, W. 2005 Pathology of Monin–Obukhov similarity in the stable boundary layer. J. Geophys. Res. Atmos. 110 (D6), D06101.CrossRefGoogle Scholar
Chimonas, G. 1999 Steps, waves and turbulence in the stably stratified planetary boundary layer. Boundary-Layer Meteorol. 90 (3), 397–421.CrossRefGoogle Scholar
Cui, G. X., Zhou, H. B., Zhang, Z. S. & Shao, L. 2004 A new dynamic subgrid eddy viscosity model with application to turbulent channel flow. Phys. Fluids 16 (8), 2835–2842.Google Scholar
Dalaudier, F. & Sidi, C. 1990 Some characteristics of the turbulent buoyancy subrange. Adv. Space Res. 10 (10), 37–40.CrossRefGoogle Scholar
Deardorff, J. W. 1980 Stratocumulus-capped mixed layers derived from a 3-dimensional model. Boundary-Layer Meteorol. 18 (4), 495–527.CrossRefGoogle Scholar
Derbyshire, S. H. 1999 Stable boundary-layer modelling: established approaches and beyond. Boundary-Layer Meteorol. 90 (3), 423–446.CrossRefGoogle Scholar
Domaradzki, J. A., Liu, W. & Brachet, M. E. 1993 An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5 (7), 1747–1759.CrossRefGoogle Scholar
Dubrulle, B., Laval, J. P., Sullivan, P. P. & Werne, J. 2002 A new dynamical subgrid model for the planetary surface layer. Part I: The model and a priori tests. J. Atmos. Sci. 59 (4), 861–876.2.0.CO;2>CrossRefGoogle Scholar
Eyink, G. L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. Part I. Smooth coarse graining. Phys. Fluids 21 (11), 115107.CrossRefGoogle Scholar
Forrer, J. & Rotach, M. W. 1997 On the turbulence structure in the stable boundary layer over the Greenland ice sheet. Boundary-Layer Meteorol. 85 (1), 111–136.Google Scholar
Germano, M. 1986 A proposal for a redefinition of the turbulent stresses in the filtered Navier–Stokes equations. Phys. Fluids 29 (7), 2323–2324.CrossRefGoogle Scholar
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
Gullbrand, J. & Chow, F. K. 2003 The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. J. Fluid Mech. 495, 323–341.CrossRefGoogle Scholar
Guo, Z. C., Dirmeyer, P. A., Koster, R. D., Bonan, G., Chan, E., Cox, P., Gordon, C. T., Kanae, S., Kowalczyk, E., Lawrence, D., Liu, P., Lu, C. H., Malyshev, S., McAvaney, B., McGregor, J. L., Mitchell, K., Mocko, D., Oki, T., Oleson, K. W., Pitman, A., Sud, Y. C., Taylor, C. M., Verseghy, D., Vasic, R., Xue, Y. K. & Yamada, T. 2006 GLACE: the global land-atmosphere coupling experiment. Part II: Analysis. J. Hydrometeorol. 7 (4), 611–625.CrossRefGoogle Scholar
Han, Z. W., Ueda, H. & An, J. L. 2008 Evaluation and intercomparison of meteorological predictions by five MM5-PBL parameterizations in combination with three land-surface models. Atmos. Environ. 42 (2), 233–249.CrossRefGoogle Scholar
Handorf, D., Foken, T. & Kottmeier, C. 1999 The stable atmospheric boundary layer over an Antarctic ice sheet. Boundary-Layer Meteorol. 91 (2), 165–189.CrossRefGoogle Scholar
Higgins, C. W., Meneveau, C. & Parlange, M. B. 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 (3), 360–375.CrossRefGoogle Scholar
Higgins, C. W., Meneveau, C. & Parlange, M. B. 2009 Geometric alignments of the subgrid-scale force in the atmospheric boundary layer. Boundary-Layer Meteorol. 132 (1), 1–9.CrossRefGoogle Scholar
Higgins, C. W., Parlange, M. B. & Meneveau, C. 2003 Alignment trends of velocity gradients and subgrid-scale fluxes in the turbulent atmospheric boundary layer. Boundary-Layer Meteorol. 109 (1), 59–83.CrossRefGoogle Scholar
Horst, T. W., Kleissl, J., Lenschow, D. H., et al. 2004 HATS: field observations to obtain spatially filtered turbulence fields from crosswind arrays of sonic anemometers in the atmospheric surface layer. J. Atmos. Sci. 61 (13), 1566–1581.2.0.CO;2>CrossRefGoogle Scholar
Kaimal, J. C. & Finnigan, J. J. 1994 Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press.CrossRefGoogle Scholar
Kaimal, J. C., Izumi, Y., Wyngaard, J. C. & Cote, R. 1972 Spectral characteristics of surface-layer turbulence. Q. J. R. Meteorol. Soc. 98 (417), 563–589.Google Scholar
Katul, G., Hsieh, C. I. & Sigmon, J. 1997 Energy-inertial scale interactions for velocity and temperature in the unstable atmospheric surface layer. Boundary-Layer Meteorol. 82 (1), 49–80.CrossRefGoogle Scholar
King, J. C., Connolley, W. M. & Derbyshire, S. H. 2001 Sensitivity of modelled Antarctic climate to surface and boundary-layer flux parametrizations. Q. J. R. Meteorol. Soc. 127 (573), 779–794.Google Scholar
Kleissl, J., Kumar, V., Meneveau, C. & Parlange, M. B. 2006 Numerical study of dynamic Smagorinsky models in large-eddy simulation of the atmospheric boundary layer: validation in stable and unstable conditions. Water Resour. Res. 42 (6), W06D10.CrossRefGoogle Scholar
Kleissl, J., Meneveau, C. & Parlange, M. B. 2003 On the magnitude and variability of subgrid-scale eddy-diffusion coefficients in the atmospheric surface layer. J. Atmos. Sci. 60 (19), 2372–2388.2.0.CO;2>CrossRefGoogle Scholar
Kleissl, J., Parlange, M. B. & Meneveau, C. 2004 Field experimental study of dynamic Smagorinsky models in the atmospheric surface layer. J. Atmos. Sci. 61 (18), 2296–2307.2.0.CO;2>CrossRefGoogle Scholar
Kosovic, B. 1997 Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers. J. Fluid Mech. 336, 151–182.CrossRefGoogle Scholar
Kosovic, B. & Curry, J. A. 2000 A large eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci. 57 (8), 1052–1068.2.0.CO;2>CrossRefGoogle Scholar
Koster, R. D., Guo, Z. C., Dirmeyer, P. A., Bonan, G., Chan, E., Cox, P., Davies, H., Gordon, C. T., Kanae, S., Kowalczyk, E., Lawrence, D., Liu, P., Lu, C. H., Malyshev, S., McAvaney, B., Mitchell, K., Mocko, D., Oki, T., Oleson, K. W., Pitman, A., Sud, Y. C., Taylor, C. M., Verseghy, D., Vasic, R., Xue, Y. K. & Yamada, T. 2006 GLACE: the global land-atmosphere coupling experiment. Part I: Overview. J. Hydrometeorol. 7 (4), 590–610.CrossRefGoogle Scholar
Kumar, V., Kleissl, J., Meneveau, C. & Parlange, M. B. 2006 Large-eddy simulation of a diurnal cycle of the atmospheric boundary layer: atmospheric stability and scaling issues. Water Resour. Res. 42 (6), W06D09.CrossRefGoogle Scholar
Kunkel, G. J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375–402.CrossRefGoogle Scholar
Lilly, D. K. 1967 The representation of small scale turbulence in numerical simulation experiments. In IBM Scientific Computing Symposium on Environmental Sciences, White Plains, NY, pp. 195–209.Google Scholar
Mahrt, L. 1998 Stratified atmospheric boundary layers and breakdown of models. Theor. Comput. Fluid Dyn. 11 (3–4), 263–279.CrossRefGoogle Scholar
Mahrt, L. 1999 Stratified atmospheric boundary layers. Boundary-Layer Meteorol. 90 (3), 375–396.CrossRefGoogle Scholar
Malhi, Y. S. 1995 The significance of the dual solutions for heat fluxes measured by the temperature fluctuation method in stable conditions. Boundary-Layer Meteorol. 74 (4), 389–396.CrossRefGoogle Scholar
Marusic, I., Kunkel, G. J. & Porte-Agel, F. 2001 Experimental study of wall boundary conditions for large-eddy simulation. J. Fluid Mech. 446, 309–320.CrossRefGoogle Scholar
Mason, P. J. 1989 Large-eddy simulation of the convective atmospheric boundary layer. J. Atmos. Sci. 46 (11), 1492–1516.2.0.CO;2>CrossRefGoogle Scholar
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stresses – necessary conditions and experimental tests. Phys. Fluids 6 (2), 815–833.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Metais, O. & Herring, J. R. 1989 Numerical simulations of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202, 117–148.CrossRefGoogle Scholar
Mirocha, J. D., Kosovic, B. & Curry, J. A. 2005 Vertical heat transfer in the lower atmosphere over the Arctic Ocean during clear-sky periods. Boundary-Layer Meteorol. 117 (1), 37–71.CrossRefGoogle Scholar
Moeng, C. H. 1984 A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.2.0.CO;2>CrossRefGoogle Scholar
Nakamura, R. & Mahrt, L. 2005 A study of intermittent turbulence with cases-99 tower measurements. Boundary-Layer Meteorol. 114 (2), 367–387.Google Scholar
Pahlow, M., Parlange, M. B. & Porte-Agel, F. 2001 On Monin–Obukhov similarity in the stable atmospheric boundary layer. Boundary-Layer Meteorol. 99 (2), 225–248.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
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 (1), 81–105.CrossRefGoogle Scholar
Porte-Agel, F., Meneveau, C. & Parlange, M. B. 2000 a A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
Porte-Agel, F., Pahlow, M., Meneveau, C. & Parlange, M. B. 2001 a Atmospheric stability effect on subgrid-scale physics for large-eddy simulation. Adv. Water Resour. 24 (9–10), 1085–1102.Google Scholar
Porte-Agel, F., Parlange, M. B., Meneveau, C. & Eichinger, W. E. 2001 b A priori field study of the subgrid-scale heat fluxes and dissipation in the atmospheric surface layer. J. Atmos. Sci. 58 (18), 2673–2698.2.0.CO;2>CrossRefGoogle Scholar
Porte-Agel, F., Parlange, M. B., Meneveau, C., Eichinger, W. E. & Pahlow, M. 2000 b Subgrid scale dissipation in the atmospheric surface layer: effects of stability and filter dimension. J. Hydrol. 1 (1), 75–87.Google Scholar
Randall, D. A. 1984 Buoyant production and consumption of turbulence kinetic-energy in cloud-topped mixed layers. J. Atmos. Sci. 41 (3), 402–413.2.0.CO;2>CrossRefGoogle Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows: An Introduction. Springer.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Part I. the basic experiment. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Steeneveld, G. J., Van de Wiel, B. J. H. & Holtslag, A. A. M. 2006 Modelling the arctic stable boundary layer and its coupling to the surface. Boundary-Layer Meteorol. 118 (2), 357–378.CrossRefGoogle Scholar
Stevens, B., Moeng, C. H. & Sullivan, P. P. 1999 Large-eddy simulations-of radiatively driven convection: sensitivities to the representation of small scales. J. Atmos. Sci. 56 (23), 3963–3984.Google Scholar
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 (1), W01409.CrossRefGoogle Scholar
Stoll, R. & Porte-Agel, F. 2008 Large-eddy simulation of the stable atmospheric boundary layer using dynamic models with different averaging schemes. Boundary-Layer Meteorol. 126 (1), 1–28.CrossRefGoogle Scholar
Sullivan, P. P., Horst, T. W., Lenschow, D. H., Moeng, C. H. & Weil, J. C. 2003 Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling. J. Fluid Mech. 482, 101–139.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C. H. 1994 A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorol. 71 (3), 247–276.CrossRefGoogle Scholar
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.Google Scholar
Tong, C. N., Wyngaard, J. C. & Brasseur, J. G. 1999 Experimental study of the subgrid-scale stresses in the atmospheric surface layer. J Atmos. Sci. 56 (14), 2277–2292.Google Scholar
Tsinober, A., Kit, E. & Dracos, T. 1992 Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169–192.Google Scholar
Venayagamoorthy, S. K. & Stretch, D. D. 2010 On the turbulent Prandtl number in homogeneous stably stratified turbulence. J. Fluid Mech. 644, 359–369.CrossRefGoogle Scholar
Vercauteren, N., Bou-Zeid, E., Parlange, M. B., Lemmin, U., Huwald, H., Selker, J. & Meneveau, C. 2008 Subgrid-scale dynamics of water vapour, heat and momentum over a lake. Boundary-Layer Meteorol. 128 (2), 205–228.Google Scholar
Vickers, D. & Mahrt, L. 1997 Quality control and flux sampling problems for tower and aircraft data. J. Atmos. Ocean. Technol. 14 (3), 512–526.2.0.CO;2>CrossRefGoogle Scholar
Vickers, D. & Mahrt, L. 2003 The co-spectral gap and turbulent flux calculations. J. Atmos. Ocean. Technol. 20 (5), 660–672.2.0.CO;2>CrossRefGoogle Scholar
Willis, G. E. & Deardorff, J. W. 1976 Use of Taylors translation hypothesis for diffusion in mixed layer. Q. J. R. Meteorol. Soc. 102 (434), 817–822.CrossRefGoogle Scholar
Wong, V. C. & Lilly, D. K. 1994 A comparison of 2 dynamic subgrid closure methods for turbulent thermal convection. Phys. Fluids 6 (2), 1016–1023.Google Scholar
Wyngaard, J. C. 1992 Atmospheric turbulence. Annu. Rev. Fluid Mech. 24, 205–233.Google Scholar
Zhang, J., Tao, B. & Katz, J. 1997 Turbulent flow measurement in a square duct with hybrid holographic PIV. Exp. Fluids 23 (5), 373–381.CrossRefGoogle Scholar