Boundary-Layer Meteorology

, Volume 135, Issue 3, pp 385–405

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


DOI: 10.1007/s10546-010-9482-3

Cite this article as:
Sorbjan, Z. & Grachev, A.A. Boundary-Layer Meteorol (2010) 135: 385. doi:10.1007/s10546-010-9482-3


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*, 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* < 0.02), “weakly-stable” (0.02 < z* < 0.6), “very-stable” (0.6 < z* < 50), and “extremely-stable” (z* > 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*)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.


CASES-99 dataFlux-based scalingFlux–gradient relationshipGradient-based scalingMonin–Obukhov similaritySHEBA dataStable boundary layer

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of PhysicsMarquette UniversityMilwaukeeUSA
  2. 2.Institute of GeophysicsPolish Academy of SciencesWarsawPoland
  3. 3.Cooperative Institute for Research in Environmental SciencesUniversity of ColoradoBoulderUSA
  4. 4.NOAA Earth System Research LaboratoryBoulderUSA