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Figure 3.20
Relationship between roughness lengths and aerodynamic resistance for
momentum transfer (left) and for heat transfer (right). The aerodynamic resistance
for heat can be interpreted as a serial combination of the aerodynamic resistance for
momentum and an excess resistance (or boundary-layer resistance) due to molecular
diffusion near the surface. Note that the vertical axis is not to scale and the dashed
proile is located within the roughness sublayer (after Garratt,
1992
).
An advantage of the use of drag laws as opposed to resistance laws is that the drag
coeficients do not depend on wind speed. The dependence of the transport on wind
speed is explicitly dealt with in the drag law itself. The drag coeficients depend
solely on observation heights, roughness lengths and stability.
3.6.3 Analytical Solutions for the Integrated
Flux-Gradient Relationships
In the previous sections an iterative procedure was needed to obtain luxes from obser-
vations of wind and temperature at two levels (see
Section 3.6.1
). However, under the
following conditions analytical solutions to the integrated lux-gradient relationships
can be found (Itier,
1982
; Riou,
1982
; DeBruin,
1982
):
•
The effect of humidity on buoyancy is ignored.
•
Wind speed and temperature are measured at the same height (at two levels, denoted as
z
1
and
z
2
).
The ratio
•
z
2
/z
1
is less than about 6.
The existence of an analytical solution implies that no iteration is needed to ind the
luxes from vertical temperature and wind speed differences. Although these ana-
lytical solutions are not exact (at least not for unstable conditions), they are fairly
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