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The Share of the Mean Turbulent Kinetic Energy in the Near-Neutral Surface Layer for High and Low Wind Speeds

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Abstract

We examine the dependence on wind speed of the share of the mean turbulent kinetic energy among the three velocity components in the near-neutral surface layer. To contrast the general behaviour and the local effects, four datasets are considered, corresponding to different surfaces and environmental conditions. For high wind speeds (i.e., wind speed \(\approx {10}\,{\hbox {ms}^{-1}}\)), the shares are well-defined and about the same for all sites. As wind speed decreases (becoming \(\approx {1}\,{\hbox { ms}^{-1}}\)), large record-to-record variability occurs giving, on average, an almost isotropic state for the horizontal velocity components. Through spectral analysis, we relate this behaviour to the low-frequency, submeso motions and to the lack of conditions required by Reynolds averaging. The implications for modelling are also discussed, showing that the wind speed, or a related quantity, must be accounted for, besides stability, in second-order closures.

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References

  • Acevedo OC, Costa FD, Oliveira PE, Puhales FS, Degrazia GA, Roberti D (2014) The influence of submeso processes on stable boundary layer similarity relationships. J Atmos Sci 71(1):207–225

    Article  Google Scholar 

  • Acevedo OC, Mahrt L, Puhales FS, Costa FD, Medeiros LE, Degrazia GA (2016) Contrasting structures between the decoupled and coupled states of the stable boundary layer. Q J R Meteorol Soc 142(695):693–702

    Article  Google Scholar 

  • Anfossi D, Oettl D, Degrazia G, Ferrero E, Goulart A (2005) An analysis of sonic anemometer observations in low wind speed conditions. Boundary-Layer Meteorol 114:179–203

    Article  Google Scholar 

  • Bradshaw P (1967) “Inactive” motion and pressure fluctuations in turbulent boundary layers. J Fluid Mech 30(2):241–258

    Article  Google Scholar 

  • Bradshaw P (1978) Comments on horizontal velocity spectra in an unstable surface layer. J Atmos Sci 35(9):1768–1769

    Article  Google Scholar 

  • Cheng Y, Brutsaert W (2005) Fluxprofile relationships for wind speed and temperature in the stable atmospheric boundary layer. Boundary-Layer Meteorol 114:519–538

    Article  Google Scholar 

  • Cuxart J, Yagüe C, Morales G, Terradellas E, Orbe J, Calvo J, Fernandez A, Soler MR, Infante C, Buenestado P, Espinalt A, Joergensen HE, Rees JM, Vila J, Redondo JM, Cantalapiedra IR, Conangla L (2000) Stable atmospheric boundary-layer experiment in Spain (SABLES 98): a report. Boundary-Layer Meteorol 96:337–370

    Article  Google Scholar 

  • Falabino S, Trini Castelli S (2017) Estimating wind velocity standard deviation values in the inertial sublayer from observations in the roughness sublayer. Meteorol Atmos Phys 129(1):83–98

    Article  Google Scholar 

  • de Franceschi M, Zardi D, Tagliazucca M, Tampieri F (2009) Analysis of second order moments in surface layer turbulence in an alpine valley. Q J R Meteorol Soc 135:1750–1765

    Article  Google Scholar 

  • Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2013) The critical richardson number and limits of applicability of local similarity theory in the stable boundary layer. Boundary-Layer Meteorol 147:51–82

    Article  Google Scholar 

  • Ha KJ, Hyun YK, Oh HM, Kim KE, Mahrt L (2007) Evaluation of boundary layer similarity theory for stable conditions in cases-99. Mon Weather Rev 135(10):3474–3483

    Article  Google Scholar 

  • Hanna SR (1982) Application in air pollution modelling. D. Reidel Publishing Company, Dordrecht

    Google Scholar 

  • Hanna SR (1983) Lateral turbulence intensity and plume meandering during stable conditions. J Clim Appl Meteorol 22(8):1424–1430

    Article  Google Scholar 

  • Hanna SR (1990) Lateral dispersion in light-wind stable conditions. Il Nuovo Cimento C 13:889–894

    Article  Google Scholar 

  • Högström U, Hunt JCR, Smedman AS (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103:101–124

    Article  Google Scholar 

  • Howell JF, Mahrt L (1997) Multiresolution flux decomposition. Boundary-Layer Meteorol 83:117137

    Article  Google Scholar 

  • Howell JF, Sun J (1999) Surface-layer fluxes in stable conditions. Boundary-Layer Meteorol 90:495520

    Article  Google Scholar 

  • Hunt J (1984) Turbulence structure in thermal convection and shear-free boundary layers. J Fluid Mech 138:161–184

    Article  Google Scholar 

  • Hunt J, Spalart P, Mansour N (1987) A general form for the dissipation length scale in turbulent shear flows. In: Studying turbulence using numerical simulation databases. Proceedings of the 1987 Summer Program, Stanford University, pp 179–184

  • Isichenko MB (1992) Percolation, statistical topography, and transport in random media. Rev Modern Phys 64(4):961–1043

    Article  Google Scholar 

  • Joffre SM, Laurila T (1988) Standard deviations of wind speed and direction from observations over a smooth surface. J Appl Meteorol 27(5):550–561

    Article  Google Scholar 

  • Kaimal J (1978) Horizontal velocity spectra in an unstable surface layer. J Atmos Sci 35(1):18–24

    Article  Google Scholar 

  • Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows. Their structure and measurement. Oxford University Press, Oxford

    Google Scholar 

  • Kaimal JC, Wyngaard JC, Izumi Y, Coté OR (1972) Spectral characteristics of surface-layer turbulence. Q J R Meteorol Soc 98:563–589

    Article  Google Scholar 

  • Liang J, Zhang L, Wang Y, Cao X, Zhang Q, Wang H, Zhang B (2014) Turbulence regimes and the validity of similarity theory in the stable boundary layer over complex terrain of the Loess Plateau, China. J Geophys Res: Atmos 119:6009–6021. https://doi.org/10.1002/2014JD021510

  • Louis J, Weill A, Vidal-Madjar D (1983) Dissipation length in stable layers. Boundary-Layer Meteorol 25(3):229–243

    Article  Google Scholar 

  • Mahrt L (2007) Weak-wind mesoscale meandering in the nocturnal boundary layer. Envirion Fluid Mech 7(4):331–347

    Article  Google Scholar 

  • Mahrt L (2014) Stably stratified atmospheric boundary layers. Annu Rev Fluid Mech 46:23–45. https://doi.org/10.1146/annurev-fluid-010313-141354

    Article  Google Scholar 

  • Mahrt L, Richardson S, Seaman N, Stauffer DR (2012) Turbulence in the nocturnal boundary layer with light and variable winds. Q J R Meteorol Soc 138:1430–1439

    Article  Google Scholar 

  • Mahrt L, Thomas C, Richardson S, Seaman N, Stauffer DR, Zeeman M (2013) Non-stationary generation of weak turbulence for very stable and weak-wind conditions. Boundary-Layer Meteorol 147:179–199

    Article  Google Scholar 

  • Mahrt L, Sun J, Stauffer DR (2015) Dependence of turbulent velocities on wind speed and stratification. Boundary-Layer Meteorol 155:5571. https://doi.org/10.1007/s10546-014-9992-5

    Article  Google Scholar 

  • Maturilli M, Herber A, König-Langlo G (2013) Climatology and time series of surface meteorology in ny-ålesund, svalbard. Earth Syst Sci Data 5(1):155

    Article  Google Scholar 

  • Mauritsen T, Svensson G (2007) Observations of stably stratified shear-driven atmospheric turbulence at low and high Richardson numbers. J Atmos Sci 64:645–655

    Article  Google Scholar 

  • Mauritsen T, Svensson G, Zilitinkevich SS, Esau IN, Enger L, Grisogono B (2007) A total turbulent energy closure model for neutrally and stably stratified atmospheric boundary layers. J Atmos Sci 64:4113–4126

    Article  Google Scholar 

  • Mazzola M, Viola AP, Lanconelli C, Vitale V (2016) Atmospheric observations at the Amundsen–Nobile climate change tower in Ny-Ålesund Svalbard. Rendiconti Lincei 27(1):7–18

    Article  Google Scholar 

  • Monin A, Obukhov A (1954) Basic laws of turbulent mixing in the surface layer of the atmosphere. Contrib Geophys Inst Acad Sci USSR 151(163):e187

    Google Scholar 

  • Monin AS, Yaglom AM (1971) Statistical fluid mechanics, vol I. MIT Press, Cambridge

    Google Scholar 

  • Moraes OL, Acevedo OC, Degrazia GA, Anfossi D, da Silva R, Anabor V (2005) Surface layer turbulence parameters over a complex terrain. Atmos Environ 39:3103–3112

    Article  Google Scholar 

  • Mortarini L, Anfossi D (2015) Proposal of an empirical velocity spectrum formula in low-wind speed conditions. Q J R Meteorol Soc 141(686):85–97

    Article  Google Scholar 

  • Mortarini L, Ferrero E, Falabino S, Trini Castelli S, Richiardone R, Anfossi D (2013) Low-frequency processes and turbulence structure in a perturbed boundary layer. Q J R Meteorol Soc 139(673):1059–1072

    Article  Google Scholar 

  • Mortarini L, Stefanello M, Degrazia G, Roberti D, Castelli ST, Anfossi D (2016) Characterization of wind meandering in low-wind-speed conditions. Boundary-Layer Meteorol 161(1):165–182

    Article  Google Scholar 

  • Nakanishi M (2001) Improvement of the mellor-yamada turbulence closure model based on large-eddy simulation data. Boundary-Layer Meteorol 99(3):349–378

    Article  Google Scholar 

  • Nieuwstadt FTM (1984) The turbulent structure of the stable, nocturnal boundary layer. J Atmos Sci 41:2202–2216

    Article  Google Scholar 

  • Obukhov A (1971) Turbulence in an atmosphere with a non-uniform temperature. Boundary-Layer Meteorol 2(1):7–29

    Article  Google Scholar 

  • Olesen HR, Larsen SE, Hojstrup J (1984) Modelling velocity spectra in the lower part of the planetary boundary layer. Boundary-Layer Meteorol 29:285–312

    Article  Google Scholar 

  • Pahlow M, Parlange M, Porte-Agel F (2001) On Monin–Obukhov similarity in the stable atmospheric boundary layer. Boundary-Layer Meteorol 99:225–248

    Article  Google Scholar 

  • Rotta JC (1951) Statisthe Theorie nichthomogener Turbulenz. Z Phys 129:547–572

    Article  Google Scholar 

  • San José R, Casanova J, Viloria RE, Casanova J (1985) Evaluation of the turbulent parameters of the unstable surface boundary layer outside Businger’s range. Atmos Environ (1967) 19(10):1555–1561

    Article  Google Scholar 

  • Smith F, Abbott P (1961) Statistics of lateral gustiness at 16 m above ground. Q J R Meteorol Soc 87(374):549–561

    Article  Google Scholar 

  • Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Alphen aan den Rijn

    Book  Google Scholar 

  • Sun J, Mahrt L, Banta RM, Pichugina YL (2012) Turbulence regimes and turbulence intermittency in the stable boundary layer during cases-99. J Atmos Sci 69(1):338–351

    Article  Google Scholar 

  • Sun J, Lenschow DH, LeMone MA, Mahrt L (2016) The role of large-coherent-eddy transport in the atmospheric surface layer based on cases-99 observations. Boundary-Layer Meteorol 160(1):83–111

    Article  Google Scholar 

  • Tampieri F (2017) Turbulence and dispersion in the planetary boundary layer. Springer International, Berlin

    Book  Google Scholar 

  • Taylor GI (1921) Diffusion by continuous movements. Proc Lond Math Soc 20:196–211

    Google Scholar 

  • Thomson DJ (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180:529–556

    Article  Google Scholar 

  • Townsend A (1961) Equilibrium layers and wall turbulence. J Fluid Mech 11(1):97–120

    Article  Google Scholar 

  • Trini Castelli S, Falabino S (2013) Analysis of the parameterization for the wind-velocity fluctuation standard deviations in the surface layer in low-wind conditions. Meteorol Atmos Phys 119:91–107. https://doi.org/10.1007/s00703-012-0219-3

    Article  Google Scholar 

  • Trini Castelli S, Falabino S, Mortarini L, Ferrero E, Richiardone R, Anfossi D (2014) Experimental investigation of surface-layer parameters in low wind-speed conditions in a suburban area. Q J R Meteorol Soc 140(683):2023–2036

    Article  Google Scholar 

  • Troen I, Mahrt L (1986) A simple model of the atmospheric boundary layer: sensitivity to surface evaporation. Boundary-Layer Meteorol 37:129–148

    Article  Google Scholar 

  • Van Ulden A, Wieringa J (1996) Atmospheric boundary layer research at cabauw. In: Boundary-layer meteorology 25th anniversary vol, 1970–1995, Springer, pp 39–69

  • Verkaik J, Holtslag A (2007) Wind profiles, momentum fluxes and roughness lengths at cabauw revisited. Boundary-Layer Meteorol 122(3):701–719

    Article  Google Scholar 

  • Vickers D, Mahrt L (2003) The cospectral gap and turbulent flux calculations. J Atmos Ocean Technol 20:660–672

    Article  Google Scholar 

  • Vickers D, Mahrt L (2006) A solution for flux contamination by mesoscale motions with very weak turbulence. Boundary-Layer Meteorol 118(3):431–447

    Article  Google Scholar 

  • Vickers D, Mahrt L (2007) observations of the cross-wind velocity variance in the stable boundary layer. Envirion Fluid Mech 7:55–71

    Article  Google Scholar 

  • Van de Wiel B, Moene A, Jonker H, Baas P, Basu S, Donda J, Sun J, Holtslag A (2012) The minimum wind speed for sustainable turbulence in the nocturnal boundary layer. J Atmos Sci 69(11):3116–3127

    Article  Google Scholar 

  • Wilson JD (2008) Monin-obukhov functions for standard deviations of velocity. Boundary-Layer Meteorol 129:353–369

    Article  Google Scholar 

  • Yadav AK, Raman S, Sharan M (1996) Surface layer turbulence spectra and dissipation rates during low winds in tropics. Boundary-Layer Meteorol 79(3):205–223

    Article  Google Scholar 

  • Yagüe C, Viana S, Maqueda G, Redondo JM (2006) Influence of stability on the flux-profile relationships for wind speed, \(\phi _m\), and temperature, \(\phi _h\), for the stable atmospheric boundary layer. Nonlinear Proc Geophys 13:185–203

    Article  Google Scholar 

  • Yamada T, Mellor G (1975) A simulation of the Wangara atmospheric boundary layer data. J Atmos Sci 32(12):2309–2329

    Article  Google Scholar 

  • Zilitinkevich SS, Esau IN (2007) Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer. Boundary-Layer Meteorol 125:193–205

    Article  Google Scholar 

  • Zilitinkevich SS, Hunt JCR, Esau IN, Grachev AA, Lalas DP, Akylas E, Tombrou M, Fairall CW, Fernando HJS, Baklanov A, Joffre SM (2006) The influence of large convective eddies on the surface-layer turbulence. Q J R Meteorol Soc 132:1423–1456

    Article  Google Scholar 

  • Zilitinkevich SS, Elperin T, Kleeorin N, Rogachevskii I, Esau IN (2013) A hierarchy of energy- and flux-budget (EFB) turbulence closure models for stably-stratified geophysical flows. Boundary-Layer Meteorol 146:341–373

    Article  Google Scholar 

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Acknowledgements

Thanks are due to: the SABLES98 team, Prof. J.L. Casanova (Director of CIBA), and Dr. J. Peláez (for his technical support); the Korean Polar Research Institute (KOPRI), in particular Dr. T. Choi, that provided CSAT3 CCT sonic data. CY has been funded by the Spanish Government, under MINECO projects CGL2015-65627-C3-3-R (MINECO/FEDER) and CGL2016-81828-REDT.

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Schiavon, M., Tampieri, F., Bosveld, F.C. et al. The Share of the Mean Turbulent Kinetic Energy in the Near-Neutral Surface Layer for High and Low Wind Speeds. Boundary-Layer Meteorol 172, 81–106 (2019). https://doi.org/10.1007/s10546-019-00435-6

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