Boundary-Layer Meteorology

, Volume 135, Issue 3, pp 385-405

First online:

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

  • Zbigniew SorbjanAffiliated withDepartment of Physics, Marquette UniversityInstitute of Geophysics, Polish Academy of Sciences Email author 
  • , Andrey A. GrachevAffiliated withCooperative Institute for Research in Environmental Sciences, University of ColoradoNOAA Earth System Research Laboratory

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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 data Flux-based scaling Flux–gradient relationship Gradient-based scaling Monin–Obukhov similarity SHEBA data Stable boundary layer