Statistical analysis of vertical velocity and buoyancy in convective boundary layers

Convective boundary layers are governed by an interplay of vertical turbulent convection and shear-driven turbulence. Here, we investigate vertical velocity and buoyancy fields in convective boundary layers for varying atmospheric conditions by combining probability density function methods and direct numerical simulations. The evolution equations for the probability density functions of vertical velocity and buoyancy contain unclosed terms in the form of conditional averages. We estimate these terms from our direct numerical simulations data, and discuss their physical interpretation. Furthermore, using the method of characteristics, we investigate how these unclosed terms jointly determine the average evolution of a fluid element in a convective boundary layer, and how it relates to the evolution of the probability density functions of vertical velocity and buoyancy as a function of height. Thereby, our work establishes a connection between the turbulent dynamics of convective boundary layers and the resulting statistics.