Aircraft observations made in the convective boundary layer (CBL) have shown that the peak of the vertical velocity spectra occurs at a wavelength about 1.5 times the boundary layer depth (H). This implies that most of the variance is present at a characteristic length scale L ~ 1.5 H. Typically, for passive scalars the spectral peak is not located at the same wavelength as the vertical velocity, but at much higher wavelengths. This implies that the passive scalar variance is largely dominated by mesoscale fluctuations. The underlying physical mechanism that can explain the generation of mesoscale fluctuations is not yet well understood. In order to study the generation of mesoscale fluctuations we have performed a Large-Eddy Simulation of a CBL and a stratocumulus-topped boundary layer on a large horizontal domain (25.6x25.6 km^2) compared to H.

By including a bottom-up and top-down scalar to the simulation, the use of a superposition principle (which follows from the linearity of the scalar transport equation) facilitates the determination of the characteristic length scale L for an arbitrary scalar. We have investigated L as a function of height and the flux ratio r, which is defined as the ratio of the top-down and bottom-up flux. For the CBL it is found that after 10 hours of simulation a minimum size for L can be expected for scalars that have a flux ratio nearby r ~ -0.2. This is approximately the flux ratio for the buoyancy flux in the TKE equation. For quantities that have a flux ratio that significantly deviates from this number the characteristic length scale is typically about 5H. For the stratocumulus case mesoscale fluctuations are omnipresent for all flux ratios; after 8 hours of simulation the minimum value for L is about 7.5H.

The two following mechanisms are suggested to explain why mesoscale fluctuations are minimal in the CBL for r=-0.2. Firstly, whereas the bottom-up and top-down scalars possess mesoscale fluctuations, superposition demonstrates that the fluctuations at these scales then nearly fully cancel. Secondly, if the vertical flux and the mean vertical gradient have the same sign, then the prognostic variance equation dictates that the variance tends to be destroyed. This is only the case for a limited range of flux ratios.