Boundary-Layer Meteorology

, Volume 135, Issue 3, pp 385–405

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


    • Department of PhysicsMarquette University
    • Institute of GeophysicsPolish Academy of Sciences
  • Andrey A. Grachev
    • Cooperative Institute for Research in Environmental SciencesUniversity of Colorado
    • NOAA Earth System Research Laboratory

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