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0
-20
-40
-60
-80
-100
0.0
0.5
1.0
1.5
2.0
2.5
3.0
θ
(K)
Figure 3.21
Sensible heat lux as a function of vertical temperature difference, given
a ixed shear (heights are 10 and 2 m, ixed wind speed difference is 2 m s
-1
).
For other scalar luxes (e.g., evapotranspiration or CO
2
transport) expressions sim-
ilar to Eqs. (
3.47
) and (
3.50
) can be used. DeBruin et al. (
2000
) extended the above
framework to situations where temperature and wind speed are not observed at the
same height.
3.6.4 Feedback Between Stability and the Sensible
Heat Flux for Stable Conditions
The analytic solutions of the lux-gradient relationships (as presented in the previous
section) allow for an interesting analysis of the behaviour of the sensible heat lux
under stable conditions. The question is: What magnitude of the sensible heat lux is
possible at a given vertical temperature gradient?
To answer this question, we assume a ixed vertical wind speed difference ('ixed
shear', see van de Wiel et al.,
2012a
). Then Eqs. (
3.50
) and (
3.52
) give a direct solu-
tion for the sensible heat lux as a function of the vertical temperature difference. This
solution is depicted in
Figure 3.21
. The striking result is that a given sensible heat
lux can be attained with two different vertical temperature differences: a near neutral
solution (small temperature difference) and a very stable solution (large temperature
difference). The physical interpretation of this result is that in the near neutral case
the vertical temperature difference is the limiting factor for the sensible heat lux.
On the other hand, for the very stable solution, the turbulence is the limiting factor:
turbulence is so much suppressed by buoyancy that despite the large temperature dif-
ference, the lux is still small.
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