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Fedorovich-Conzemius-JAS04 - 1 FEBRUARY 2004 FEDOROVICH ET...

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1 F EBRUARY 2004 281 F E D O R O V I C H E T A L . q 2004 American Meteorological Society Convective Entrainment into a Shear-Free, Linearly Stratified Atmosphere: Bulk Models Reevaluated through Large Eddy Simulations E VGENI F EDOROVICH AND R OBERT C ONZEMIUS School of Meteorology, University of Oklahoma, Norman, Oklahoma D MITRII M IRONOV German Weather Service, Offenbach am Main, Germany (Manuscript received 19 December 2002, in final form 15 September 2003) ABSTRACT Relationships between parameters of convective entrainment into a shear-free, linearly stratified atmosphere predicted by the zero-order jump and general-structure bulk models of entrainment are reexamined using data from large eddy simulations (LESs). Relevant data from other numerical simulations, water tank experiments, and atmospheric measurements are also incorporated in the analysis. Simulations have been performed for 10 values of the buoyancy gradient in the free atmosphere covering a typical atmospheric stability range. The entrainment parameters derived from LES and relationships between them are found to be sensitive to the model framework employed for their interpretation. Methods of determining bulk model entrainment parameters from the LES output are proposed and discussed. Within the range of investigated free-atmosphere stratifications, the LES predictions of the inversion height and buoyancy increment across the inversion are found to be close to the analytical solutions for the equilibrium entrainment regime, which is realized when the rate of time change of the CBL-mean turbulence kinetic energy and the energy drain from the CBL top are both negligibly small. The zero-order model entrainment ratio of about 0.2 for this regime is generally supported by the LES data. However, the zero-order parameterization of the entrainment layer thickness is found insufficient. A set of relationships between the general-structure en- trainment parameters for typical atmospheric stability conditions is retrieved from the LES. Dimensionless constants in these relationships are estimated from the LES and laboratory data. Power-law approximations for relationships between the entrainment parameters in the zero-order jump and general-structure bulk models are evaluated based on the conducted LES. In the regime of equilibrium entrainment, the stratification parameter of the entrainment layer, which is the ratio of the buoyancy gradient in the free atmosphere to the overall buoyancy gradient across the entrainment layer, appears to be a constant of about 1.2. 1. Introduction The atmospheric convective boundary layer (CBL) is a particular type of turbulent boundary layer forced by buoyancy flux originating at the bottom of the layer (surface heating) or at its top (radiative cooling from clouds), or both. Buoyant convection is usually the main mechanism of turbulence production in the CBL, and the contribution of wind shear to the generation of tur- bulence is of secondary importance. In cases when shear
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