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Air Pollution and Turbulence: Modeling and Applications
underestimated, producing insuffi cient top-entrainment, and the inner layer is less
well mixed.
The analysis of the vertical profi les of the two contributions (K-diffusion and
counter-gradient) to the total fl ux of potential temperature reveals the reason for
the weak BL growth result of the K + C scheme (Figure 4.19). In fact, the nonlocal transport, that is, the counter-gradient term is always positive, unlike the MF
contribution in the EDMF-EMP. Thus, the buoyancy fl ux associated with topentrainment is reduced. In this example, the two contributions in the inversion
region are almost symmetrical, provoking the inexistence of top-entrainment and
the lack of BL growth. By adding nonlocal transport in the upper half BL, the
counter-gradient inhibits the top-entrainment (Figure 4.20).
1.5
1.0
0.5
0.0
299.0
299.2
299.4
299.6
299.8
θ (K)
Height (km)
LES
K + M
K + C
K
FIGURE 4.19 Vertical profi les of potential temperature from the three different parameterizations. Fifth hour average for the schemes: (K + M) EDMF-EMP, (K) K-diffusion, (K + C)
K-diffusion with counter-gradient, and the LES model.
2.0
1.5
1.0
0.5
0.0
–0.02
0.00
0.02
0.04
0.06
Height (km)
w΄θ΄ (ms
–1 K)
CG
ED
Total
FIGURE 4.20 The eED and Counter-gradient (CG) contributions for the vertical fl ux of
potential temperature. Hourly average of the 10th hour.
© 2010 by Taylor and Francis Group, LLC