A Model for a Shear-Free Convective Boundary Layer with Parameterized Capping Inversion Structure

Abstract

The paper extends Deardorff's general structure parameterization for a shear-free convective boundary layer. The model suggested employs the mixed layer hypothesis that the buoyancy (which is defined as b = g(?0 ? &rho)/?0, where ? is the density, ?0 is the reference density, and g is the acceleration due to gravity) is constant with height within the mixed layer. The buoyancy flux zero-crossing height is taken as the mixed layer depth. The vertical buoyancy profile within the capping inversion, where the buoyancy flux is negative due to entrainment, is made dimensionless, using the buoyancy difference across the inversion and its thickness as appropriate scales. The approach was first suggested by Kitaigorodskii and Miropolsky for the oceanic seasonal thermocline. The authors examine the idea against the data from atmospheric measurements, laboratory experiments with buoyancy-agitated turbulence, and large-eddy simulations. The rate equations for the mixed layer and inversion layer depths are derived using the turbulent kinetic energy equation and Deardorff's scaling hypothesis refined to account for the inversion layer structure. The constants of the model are evaluated from the data of atmospheric, oceanic, and laboratory measurements, and large-eddy simulations. The causes of divergence of the estimates based on data of different origin are discussed. The model is applied to simulate convective entrainment in laboratory experiments. A reasonable explanation for ambiguous behavior of the entrainment zone in the experiments with a two-layer fluid is suggested. The model is found to simulate transition regimes of convective entrainment in multilayer fluid strongly affected by the nonstationarity of the entrainment zone.