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

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/I >(*), z being height and I >(*) 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/I >(*) < 0.02), weakly-stable (0.02 < z/I >(*) < 0.6), very-stable (0.6 < z/I >(*) < 50), and extremely-stable (z/I >(*) > 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/I >(*))(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.