Vertical-Velocity Skewness in the Buoyancy-Driven Boundary Layer

A number of puzzling features of the skewness of the vertical velocity field, Sw(z), are found in observations and large-eddy simulations (LES) of the buoyancy-driven planetary boundary layer (PBL). For example, observations of Sw(z) in cases where the air is heated from below indicate that Sw(z) > 0 and remains relatively constant for z ≳ 0.3zi, whereas all large-eddy simulations of these cases show a continuing increase of Sw(z) with height. In cases where the air is both heated from below and cooled from above, as in some of the stratus-topped PBL cases, large-eddy simulations show a rather curious feature: Sw is positive in the upper layer and negative in the lower layer. In considering these features, it occurred to us that a theoretical model of what one should expect of the skewness distribution, even in simple situations, did not exist. Hence in the present paper we examine the skewness distributions from direct numerical simulations of several simple archetypes of buoyancy-driven turbulent flow. While these simulations do not resolve the discrepancy between LES and observations, they help in understanding the LES results, and suggest avenues for future research.