Joint Seminar: Recent Advances in the Similarity Theory of the Stable Boundary Layer

The gradient-based scaling system for the stably stratified boundary layer is introduced and examined by using data collected during the SHEBA field program in the Arctic. The resulting similarity functions for fluxes and variances are expressed in an analytical form, which is practically unaffected by self-correlation. The flux Richardson number Rf is found to be proportional to the Richardson number Ri, with the proportionality coefficient varying slightly with stability, from 1.11 to 1.47. The Prandtl number decreases from 0.9 in nearly-neutral conditions to 0.7 for larger values of Ri. The budget of the turbulent kinetic energy indicates that for Ri > 0.7, turbulence must be non-stationary and decaying or sporadic. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral”, “weakly-stable”, “very-stable”, and "extremely-stable".


Both gradient-based and flux-based similarity functions in the stable boundary layer, based on bin-averaged data, show an undesired dependence on the height at which the observations are collected. A correction of this flaw is proposed and tested through the use of data collected during the CASES-99 experiment. The correction is accomplished by employing Blackadar’s expression for the mixing length in a definition of the local similarity scale for height. As a result, the dependence of similarity functions on the Richardson number Ri is the same in the surface layer as in the layer above it.


The gradient-based similarity functions, evaluated using the SHEBA and CASES-99 data, are subsequently tested within a single-column, high-resolution, K-theory model of the stable boundary layer. The model resolves the logarithmic layer, and does not require inverting the Monin-Obukhov similarity functions in order to calculate the surface fluxes. The standard deviations of the vertical velocity and temperature, σw and σθ, as well as the dissipation rate ε, are diagnosed from the gradient-based similarity expressions. The model shows excellent agreement with LES models (Met-Office LES, and the University of Hannover LES model), tested during the GABLS intercomparison program. The model is used to study the stable boundary layer, i.e., the effects of shear, thermal stratification, subsidence, and baroclinicity, by varying the surface cooling, roughness parameter, the values of the geostrophic wind, and the Coriolis parameter.




13:30 h


Bundesstr. 53, room 022/023
Seminar Room 022/023, Ground Floor, Bundesstrasse 53, 20146 Hamburg, Hamburg


Zbigniew Sorbjan, Marquette University


Thorsten Mauritsen

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