Improving the Eddy Kinetic Energy model for planetary boundary layer description

Abstract

Results from a third-order turbulence closure scheme model and from experimental studies are used to improve the Eddy Kinetic Energy (EKE) model for the Planetary Boundary Layer (PBL).It is proposed to use two different lengths, one for mixing and one for dissipation, as well as a temperature counter-gradient in the heat flux parameterization and a corrective term in the gradient-type relation for the computation of EKE flux. Such refinements do not lead to any increase in computing cost nor to any particular difficulty for the model implementation. They however allow for significantly better results, which are in close agreement with those of much more sophisticated models, at least in the case of the convective PBL, which is mainly considered here.

Development of an Improved Turbulence Closure Model for the Atmospheric Boundary Layer

“…Although the present parameterization of the thirdorder turbulent fluxes may be less sophisticated in comparison with the one that incorporates the production of their fluxes due to buoyancy (e.g., Therry and Lacarrère 1983;Canuto et al 1994; Abdella and McFarlane 1997), the stability functions in Eqs. (67) and (68) include the buoyancy e¤ects through S M .…”

“…First-order turbulence closure models, such as the K-profile model (e.g., Troen and Mahrt 1986;Hong et al 2006), the KE (so-called one-anda-half order closure) model (e.g., Therry and Lacarrère 1983;Bougeault and Lacarrère 1989), and the standard k À e model (e.g., Hanjalic and Launder 1972), have succeeded in reproducing various flow fields. The major weakness of these models, however, is that they need somewhat empirical formulations (e.g., Deardor¤ 1972) in order to express a countergradient di¤usion process resulting from non-local transport, since they relate second-order moments to local gradients of the mean fields through eddy di¤usivities.…”

“…On the other hand, higher-order turbulence closure models can express the countergradient di¤usion by predicting secondorder moments. Among them, third-order turbulence closure models such as André et al (1978) and Cheng et al (2005) have been often used to evaluate lower-order turbulence closure models (e.g., Therry and Lacarrère 1983). The third-order turbulence closure models, however, have a large number of prognostic equations and require large computer resources.…”

Turbulence modeling in the atmospheric boundary layer: a review and some recent developments

“…For the various length scale empirical relations that have been used, the reader can refer to [7]. Therry and Lacarrere [8] as well as Lascher and Arya [9] have done an important work in this field. The most common formulation used today for the length scale in the one-equation turbulent modelling is that of Duynkerke and Driedonks [10].…”

Assessment of heat flux turbulence models for flows dominated by buoyancy effects

“…Also, there is some evidence from field observations and laboratory experiments (e.g., Therry and Lacarrère, 1983;Tsuji et al, 1993), that in buoyancy driven flows (notably, within the mixed-region of the atmospheric boundary layer, and in the thermally driven turbulent boundary layer along a vertical plate) the ratio of the vertical-stress component to the kinetic energy remains reasonably constant. This gives some support to representing normal stress components as a fraction of the turbulence energy.…”