Progress in Countre-Gradient Transport Theory

Conclusions

We have reformulated the diffusion equation in a way that includes counter-gradient effects. The Reynolds-averaged equations up to third order gives some support (in appropriate approximations) for this formulation.

The general shape of the CBL profiles is largely determined by the inhomogeneities in the turbulence profiles (variance, timescale etc.) but the extended diffusion equation (2) provides a small but essential counter-gradient contribution.

In a simulation using the third-order Reynolds-averaged equations, both bottom-up and in top-down diffusion are counter-gradient. In the top-down case the counter-gradient range is, however, limited to the lowest 5% of the CBL. The fit with the LES data is fair both for the top-down and bottom-up diffusion.

The impact of the skewness can be nicely demonstrated with the Reynolds averaged model (5a,b,c) by comparing runs with and without skewness. Though the profiles are qualitatively the same, the agreement with the data improves considerably when the skewness is taken into account (see figure 3). This conclusion is in line with the findings of Cuijpers and Holtslag (1998).