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On the turbulent Prandtl number in the stable atmospheric boundary layer

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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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Authors and Affiliations

  1. Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO, USA

    Andrey A. Grachev & P. Ola G. Persson

  2. NOAA Earth System Research Laboratory, Boulder, CO, USA

    Andrey A. Grachev, Christopher W. Fairall & P. Ola G. Persson

  3. NorthWest Research Associates, Inc. (Bellevue Division), Lebanon, NH, USA

    Edgar L Andreas

  4. Naval Postgraduate School, Monterey, CA, USA

    Peter S. Guest

Authors
  1. Andrey A. Grachev
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  2. Edgar L Andreas
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  3. Christopher W. Fairall
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  4. Peter S. Guest
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  5. P. Ola G. Persson
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Correspondence to Andrey A. Grachev.

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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

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