Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 132

the context of this topic the most important statistical quantities are the covariance
of vertical wind speed with other quantities such as temperature, humidity, CO 2 and
horizontal wind. Those covariances represent the turbulent luxes (transport) of heat,
water vapour, CO 2 and momentum that we are after.
Although the governing equations for the low of air are known (Navier-Stokes
equations), those cannot be solved for any practical atmospheric situation. Therefore,
we have to resort to the empirical similarity theory. Similarity theory is used to relate
theoretically derived dimensionless groups to each other, based on experimental data.
The resulting similarity relationships can be applied in a number of ways to derive
turbulent luxes from vertical gradients and vertical differences of, for example, wind
speed, temperature and humidity.
In Figure 3.22 , everything above 'Similarity theory' relates to the physical reality.
Everything below 'Similarity relationships' is a direct - mathematical - consequence
of the empirical similarity relationships found by combining similarity theory and
experimental data. If one would have found different similarity relationships (differ-
ent in form, or different in the values of the coeficients), the derived equations would
have been different as well.
The fact that everything in the lower part of the diagram follows mathematically
from those similarity relations does not mean that the lower part does not bear a rela-
tionship to the physical reality. On the contrary, the framework of similarity theory
enables us to analyse processes in the physical world.