Similarity Theory of the Buoyantly Interactive Planetary Boundary Layer with Entrainment

Abstract

A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable ? = z/h, where h is the physical height or thickness, where the system includes six parameters associated with surface roughness, buoyant stability of the turbulence near the surface, Coriolis effects, baroclinicity and stability of the air mass above the boundary layer. To close the system a new formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer. The model is tested in simplified versions which depend only on roughness, surface buoyancy and Coriolis effects by comparison with Clarke's planetary boundary layer wind and temperature profile observations, Arya's measurements of flat-plate boundary layers in a thermally stratified wind tunnel, and Lenschow's observations of profiles of terms in the turbulent kinetic energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.