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ln
.
κ
d
κ
d
u
κ
z
z 0 +
1
d
z
η
1
z
z i
z
η
z
z i
u ( z )
=
(2.21)
1
+
d
For neutral stability and d
=
1, Peña et al. ( 2009 ) find
η =
39 m; for d
=
1.25 they
give
37 m. The only necessary parameter in eq. ( 2.21 ) from above the surface
layer is the height of the boundary layer, z i .
η =
2.2.1.4 Internal Boundary Layers
The boundary layer flow structure tends to be in equilibrium with the surface proper-
ties underneath, which govern the vertical turbulent momentum, heat, and moisture
fluxes. When the flow transits from one surface type to another with different sur-
face properties, the flow structure has to adapt to the new surface characteristics.
This leads to the formation of an internal boundary layer (IBL, internal because
it is a process taking place within an existing boundary layer) that grows with the
distance from the transition line (Fig. 2.3 ).
An IBL with a changed dynamical structure can develop when the flow enters
an area with a different roughness (e.g. from pasture to forests or from agricul-
tural areas to urban areas). An IBL with a modified thermal structure can come into
existence when the flow enters an area with a different surface temperature (e.g.
from land to sea or from water to ice). Often dynamical and thermal changes occur
simultaneously. Vertical profiles of wind, temperature, and moisture can change at
the IBL top.
The IBL top has to be distinguished from inversions and sloping frontal surfaces
at which likewise changes in the vertical profiles of wind, temperature, and moisture
can happen. Inversions are usually horizontal and caused either by adiabatic sinking
Fig. 2.3 Formation of internal boundary layers due to changes in surface roughness length
 
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