Original Paper

Boundary-Layer Meteorology

, Volume 125, Issue 2, pp 329-341

On the turbulent Prandtl number in the stable atmospheric boundary layer

  • Andrey A. GrachevAffiliated withCooperative Institute for Research in Environmental Sciences, University of ColoradoNOAA Earth System Research Laboratory Email author 
  • , Edgar L AndreasAffiliated withNorthWest Research Associates, Inc. (Bellevue Division)
  • , Christopher W. FairallAffiliated withNOAA Earth System Research Laboratory
  • , Peter S. GuestAffiliated withNaval Postgraduate School
  • , P. Ola G. PerssonAffiliated withCooperative Institute for Research in Environmental Sciences, University of ColoradoNOAA Earth System Research Laboratory

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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.

Keywords

Richardson number SHEBA Stable boundary layer Turbulent Prandtl number