Sorbjan Z. and A. A. Grachev (June 2010): An evaluation of the flux-gradient relationship in the stable boundary layer. Boundary-Layer Meteorol., 135 (3), 385-405. doi:10.1007/s10546-010-9482-3Full text not available from this repository.
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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