We investigate by means of direct numerical simulation how large-scale circulations produce deviations from Monin-Obukhov similarity theory (MOST) in the limit of free convection, disentangling the role of large-scale downdrafts from updrafts using conditional analysis. We compare the convective boundary layer to two other free-convective flows: Rayleigh-Bénard convection with an adiabatic top lid and classical Rayleigh-Bénard convection. This serves a dual purpose: firstly, to ascertain how changes in the upper boundary conditions and thereby in the large-scale circulations modify the near-surface behaviour and secondly, to assess to what extent we can extrapolate results from idealized systems to the unstable atmospheric surface layer. Using a low-pass filter to define the large scales we find that, whilst deviations from MOST occur within large-scale downdraft regions, strong deviations also occur within large-scale updraft regions. The deviations within updrafts are independent of the filter length scale used to define the large-scale circulations, independent of whether updrafts are defined as ascending air, or as air that is both ascending and positively buoyant, and are not due to changes with height of the updraft area fraction. This suggests that even updraft properties are not just determined locally, but also by outer scales. Cold, strong downdrafts in classical Rayleigh-Bénard convection notably modify the near-surface behaviour compared to the other two systems. For the moderate Reynolds numbers considered, Rayleigh-Bénard convection with an adiabatic top lid thus seems more appropriate than classical Rayleigh-Bénard convection for studying the unstable atmospheric surface layer in the limit of free convection.

In reality though, these circulations are far from uniform in the zonal and meridional directions, and show considerable spatial variability, leading to the concept of local Hadley and Walker circulations (e.g., Schwendike et al., 2014, 2015). One of the most important sources of variability in the Tropics is the Madden-Julian Oscillation (MJO), which consists of a dipole of enhanced and suppressed convection that moves eastward from the tropical Indian Ocean to the Western Pacific with a period of 30-60 days (e.g., Madden &

Conventional analysis has shown that strong wind shear enhances the entrainment buoyancy flux in the convective boundary layer. By conditioning the entrainment zone into regions of turbulent (i.e. strongly vortical) and non-turbulent (i.e. weakly vortical) flow, some unexpected aspects of this process are revealed. It is found that turbulent regions contribute the most to the entrainment buoyancy flux, but that as wind shear increases, the magnitude of the buoyancy flux in turbulent regions remains approximately constant, or even decreases, despite substantially stronger buoyancy fluctuations. The reason is that the correlation between buoyancy and vertical velocity fluctuations decreases with increasing wind shear, to the extent that it compensates the stronger buoyancy fluctuations. In free convection, this correlation is high because the vertical velocity is mainly determined by the buoyancy force acting in the same direction. Under strong shear conditions, buoyancy is no longer the only external source of vertical velocity fluctuations and their correlation consequently decreases. Hence, shear enhancement of the buoyancy flux in the entrainment zone is primarily due to an increase of the turbulent area fraction, rather than a change of flux inside the turbulent regions.

The magnitude of the entrainment buoyancy flux, and hence the growth rate of the convective boundary layer, does not increase monotonically with wind shear. Explanations for this have previously been based on wind-shear effects on the turbulence kinetic energy. By distinguishing between turbulent and non-turbulent regions, we provide an alternative explanation based on two competing wind-shear effects: the initial decrease in the correlation between buoyancy and vertical velocity fluctuations, and the increase in the turbulent area fraction. The former is determined by the change in the dominant forcing; without wind shear, buoyancy fluctuations drive vertical velocity fluctuations and the two are thus highly correlated; with wind shear, vertical velocity fluctuations are partly determined by horizontal velocity fluctuations via the transfer of kinetic energy through the pressure–strain correlation, thus reducing their correlation with the buoyancy field. The increasing turbulent area fraction, on the other hand, is determined by the increasing shear production of turbulence kinetic energy inside the entrainment zone. We also show that the dependence of these conditional statistics on the boundary-layer depth and on the magnitude of the wind shear can be captured by a single non-dimensional variable, which can be interpreted as an entrainment-zone Froude number.