Abstract
This study focuses on the behaviour of the turbulent Prandtl number, Pr t , in the stable atmospheric boundary layer (SBL) based on measurements made during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA). It is found that Pr t increases with increasing stability if Pr t is plotted vs. gradient Richardson number, Ri; but at the same time, Pr t decreases with increasing stability if Pr t is plotted vs. flux Richardson number, Rf, or vs. ζ = z/L. This paradoxical behaviour of the turbulent Prandtl number in the SBL derives from the fact that plots of Pr t vs. Ri (as well as vs. Rf and ζ) for individual 1-h observations and conventional bin-averaged values of the individual quantities have built-in correlation (or self-correlation) because of the shared variables. For independent estimates of how Pr t behaves in very stable stratification, Pr t is plotted against the bulk Richardson number; such plots have no built-in correlation. These plots based on the SHEBA data show that, on the average, Pr t decreases with increasing stability and Pr t < 1 in the very stable case. For specific heights and stabilities, though, the turbulent Prandtl number has more complicated behaviour in the SBL.
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References
Andreas EL (2002). Parameterizing scalar transfer over snow and ice: a review. J Hydormeterol 3: 417–432
Andreas EL and Hicks BB (2002). Comments on ‘Critical test of the validity of Monin-Obukhov similarity during convective conditions’. J Atmos Sci 59: 2605–2607
Andreas EL, Claffey KJ, Jordan RE, Fairall CW, Guest PS, Persson POG and Grachev AA (2006). Evaluations of the von Kármán constant in the atmospheric surface layer. J Fluid Mech 559: 117–149
Baas P, Steeneveld GJ, Holtslag AAM and Wiel BJH (2006). Exploring self-correlation in flux-gradient relationships for stably stratified conditions. J Atmos Sci 63(11): 3045–3054
Basu S and Porté-Agel F (2006). Large-eddy simulation of stably stratified atmospheric boundary layer turbulence: a scale-dependent dynamic modeling approach. J Atmos Sci 63(8): 2074–2091
Beare RJ, MacVean MK, Holtslag AAM, Cuxart J, Esau I, Golaz J-C, Jimenez MA, Khairoutdinov M, Kosovic B, Lewellen D, Lund TS, Lundquist JK, McCabe A, Moene AF, Noh Y, Raasch S and Sullivan P (2006). An intercomparison of large-eddy simulations of the stable boundary layer. Boundary-Layer Meteorol 118(2): 247–272
Beljaars ACM and Holtslag AAM (1991). Flux parameterization over land surfaces for atmospheric models. J Appl Meteorol 30: 327–341
Frenzen P and Vogel CA (1995a). On the magnitude and apparent range of variation of the von Kármán constant in the atmospheric surface layer. Boundary-Layer Meteorol 72: 371–392
Frenzen P and Vogel CA (1995b). A further note ‘On the magnitude and apparent range of variation of the von Kármán constant’. Boundary-Layer Meteorol 73: 315–317
Grachev AA, Fairall CW, Persson, POG, Andreas EL, Guest PS, Jordan RE (2003) Turbulence decay in the stable arctic boundary layer. In: seventh conference on polar meteorology and oceanography and joint symposium on high-latitude climate variations. Amer. Meteorol. Soc., Hyannis, Massachusetts, Preprint CD-ROM
Grachev AA, Fairall CW, Persson POG, Andreas EL and Guest PS (2005). Stable boundary-layer scaling regimes: the SHEBA data. Boundary-Layer Meteorol 116(2): 201–235
Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2007) SHEBA flux-profile relationships in the stable atmospheric boundary layer. Boundary-Layer Meteorol (in Press) DOI: 10.1007/s10546-007-9177-6 .
Hicks BB (1978). Comments on ‘The characteristics of turbulent velocity components in the surface layer under convective conditions by H A Panofsky, et al. Boundary-Layer Meteorol 15(2): 255–258
Howell JF and Sun J (1999). Surface-layer fluxes in stable conditions. Boundary-Layer Meteorol 90(3): 495–520
Kim J and Mahrt L (1992). Simple formulation of turbulent mixing in the stable free atmosphere and nocturnal boundary layer. Tellus 44(5): 381–394
Klipp CL and Mahrt L (2004). Flux-gradient relationship, self-correlation and intermittency in the stable boundary layer. Quart J Roy Meteorol Soc 130(601): 2087–2103
Kondo J, Kanechika O and Yasuda N (1978). Heat and momentum transfers under strong stability in the atmospheric surface layer. J Atmos Sci 35: 1012–1021
Lange B, Johnson HK, Larsen S, Højstrup J, Kofoed-Hansen H and Yelland MJ (2004). On detection of a wave age dependency for the sea surface roughness. J Phys Oceanogr 34(6): 1441–1458
Mahrt L, Sun J, Blumen W, Delany T and Oncley S (1998). Nocturnal boundary-layer regimes. Boundary-Layer Meteorol 88: 255–278
Monin AS and Yaglom AM (1971). Statistical fluid mechanics: mechanics of turbulence, vol. 1. MIT Press, Cambridge, MA pp, 769
Monti P, Fernando HJS, Princevac M, Chen WC, Kowalewski TA and Pardyjak ER (2002). Observation of flow and turbulence in the nocturnal boundary layer over a slope. J Atmos Sci 59(17): 2513–2534
Ohya Y (2001). Wind tunnel study of atmospheric stable boundary layers over a rough surface. Boundary-Layer Meteorol 98(1): 57–82
Oncley SP, Friehe CA, Larue JC, Businger JA, Itswiere EC and Chang SS (1996). Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions. J Atmos Sci 53: 1029–1044
Persson POG, Fairall CW, Andreas EL, Guest PS and Perovich DK (2002). Measurements near the atmospheric surface flux group tower at SHEBA: near-surface conditions and surface energy budget. J Geophys Res 107(C10): 8045 DOI: 10.1029/2000JC000705
Strang EJ and Fernando HJS (2001). Vertical mixing and transports through a stratified shear layer. J Phys Oceanog 31(8): 2026–2048
Sukoriansky S, Galperin B and Perov V (2006). A quasi-normal scale elimination model of turbulence and its application to stably stratified flows. Nonlinear Processes Geophys 13(1): 9–22
Ueda H, Mitsumoto S and Komori S (1981). Buoyancy effects on the turbulent transport processes in the lower atmosphere. Quart J Roy Meteorol Soc 107(453): 561–578
Yagüe C, Maqueda G and Rees JM (2001). Characteristics of turbulence in the lower atmosphere at Halley IV Station, Antarctica. Dyn Atmos Ocean 34: 205–223
Zilitinkevich SS (2002). Third-order transport due to internal waves and non-local turbulence in the stably stratified surface layer. Quart J Roy Meteorol Soc 128: 913–925
Zilitinkevich S and Calanca P (2000). An extended similarity-theory for the stably stratified atmospheric surface layer. Quart J Roy Meteorol Soc 126: 1913–1923
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Grachev, A.A., Andreas, E.L., Fairall, C.W. et al. On the turbulent Prandtl number in the stable atmospheric boundary layer. Boundary-Layer Meteorol 125, 329–341 (2007). https://doi.org/10.1007/s10546-007-9192-7
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DOI: https://doi.org/10.1007/s10546-007-9192-7