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Fig. 3.21 Principal sketch of wind profiles within internal boundary layers developing over step-
changes in surface roughness. h denotes the overall IBL height, h
1
the height in the top kink in the
wind profile, h
2
the height of the lower equilibrium layer underneath which the flow is in
equilibrium with the new surface roughness. s?r means a transition from smooth to rough and
r?s a transition from rough to smooth
properties, the single IBL loses its identity and multiple IBLs can no longer be
distinguished from each other. This height is also called the blending height.
The height of the top of an IBL is a question of definition (see Fig.
3.21
). h
2
gives the height of the layer which is completely in a new equilibrium with the
new surface type. This layer is also called the equilibrium layer. h
1
gives the height
where the wind profile has its upper kink and matches the undisturbed upstream
wind profile. h gives the height in which vertical extrapolations of the near surface
equilibrium wind profiles upstream and downstream of the step change meet. The
layer between h
2
and h is called the transition layer. The dashed curve in Fig.
3.21
displays schematically the wind profile in the IBL of a smooth-to-rough transition,
the dash-dotted line the profile in a rough-to-smooth transition. Real wind profiles
show smoother transitions between the vertical layers and exhibit an inflection
point between h
2
and h
1
.
The description of the height of such IBLs has been the subject of research and
data evaluation for several decades now. Savelyev and Taylor (
2005
) have sum-
marized this work in a review in which they list 20 formulae for the IBL height from
earlier publications and add another two. Recently Floors et al. (
2011
) have revisited
the issue having available measurements from upstream and downstream of the
change in surface properties. They investigated internal boundary layers forming at
the Danish west coast by analysing data from the Horns Rev meteorological tower
about 15 km off the coast in the North Sea and the 160 m high Høvsøre onshore mast
1.8 km away from the coastline. Floors et al. found that the dispersion analogy of
Miyake (
1965
) gives the most suitable formula for the IBL height:
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