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An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer

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Abstract

Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ*, z being height and Λ* the local Obukhov length. The resulting functions are expressed in an analytical form, which is essentially unaffected by self-correlation, when thermal stratification is strong. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral” (0 < z/Λ* < 0.02), “weakly-stable” (0.02 < z/Λ* < 0.6), “very-stable” (0.6 < z/Λ* < 50), and “extremely-stable” (z/Λ* > 50). The flux-based similarity functions for gradients are constant in “nearly-neutral” conditions. In the “very-stable” regime, the dimensionless gradients are exponential, and proportional to (z/Λ*)3/5. The existence of scaling laws in “extremely-stable” conditions is doubtful. The Prandtl number Pr decreases from 0.9 in nearly-neutral conditions and to about 0.7 in the very-stable regime. The necessary condition for the presence of steady-state turbulence is Ri < 0.7.

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Authors and Affiliations

  1. Department of Physics, Marquette University, Milwaukee, WI, 53201-1881, USA

    Zbigniew Sorbjan

  2. Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland

    Zbigniew Sorbjan

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

    Andrey A. Grachev

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

    Andrey A. Grachev

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  1. Zbigniew Sorbjan
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  2. Andrey A. Grachev
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Correspondence to Zbigniew Sorbjan.

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Sorbjan, Z., Grachev, A.A. An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer. Boundary-Layer Meteorol 135, 385–405 (2010). https://doi.org/10.1007/s10546-010-9482-3

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