For even stronger winds with low thermal stability (F r about 1.7), the natural
wavelength is longer than the hill height. This causes separation of the downwind
boundary layer of the hill, delivering a cavity zone, in the opposite direction to the
main flow. The drag force associated with the flow over a hill is maximum for the
resonance state (F r = 1). This force is lower if F r is lower than 1 and for the
separation boundary layer caused by natural waves of greater wavelength (F r > 1)
(Stull 1994).
5.5.2 Flow Under Neutral Conditions
The Froude number tends to infinity under neutral stability, and so cannot be used
for the characterization of the atmospheric flow. Over smooth topography, flow
separation and the formation of cavity areas are like those described above for
urban canopies. These processes are lighter and may even be absent (Taylor et al.
1987). Under neutrality, the streamlines are disturbed upstream and above the hill at
about threefold the hill height. Beyond this zone, the flow is not affected by the hill.
At the hilltop the streamlines converged, causing the wind to accelerate. Below the
downwind hill slope, strong winds cause a cavity area related to the separation of
the boundary layer and to the beginning of turbulent wakes. Their height is about
the same as the height of the hill, but increases in size along decreasing with
turbulence intensity, increasing downwards.
In general, airflow accelerates as it moves upstream over the top of the hills. The
acceleration factor A f , or fractional speedup is defined as the ratio Duðx; zÞ=u 0 ðzÞ,
where Duðx; zÞ is the difference between the mean horizontal streamwise velocity at
height z and u 0 ðzÞ. The u 0 ðzÞ is a reference velocity, at a downwind distance where
it is not influenced by the hill (Kaimal & Finnigan 1994). This A f factor decreases
with an increase in height (Fig. 5.12b) and varies between 1 and 2.5, depending on
hill shape, slope, and the ratio between the width and height. The magnitude of
speedup in hilltop is relevant for topics as diverse as wind power facilities or
estimation of wind load in buildings.
In the case of flow around a cone-shaped hill, rather than accelerating over the
top, the flow passes laterally around the surface (Fig. 5.12c) which remains
unchanged relatively to the flat surface (Rohatgi and Nelson 1994).
The highest rates of acceleration are seen around lightly sloped
three-dimensional hills (Arya 1988). The flow moving at oblique angles to the hills
is characterized by lateral vortices and a helical turbulent flow wake.
The mean hill width L 1/2 , is defined as the horizontal distance from the hill peak
to a point corresponding to half the peak height (Fig. 5.12a). For slightly sloping
hills, wind acceleration can be about twice the ratio of the hill height and L 1/2 . This
ratio is about 1.6 for isolated hills (Taylor and Teunissen 1987). For very slightly
sloping hills (height 100 m and L 1/2 about 250 m), wind acceleration above the top
will be about 60% compared to normal conditions.
Such data is relevant to the installation of wind turbines. The height at maximum
acceleration, Dz max , can be estimated as follows (Stull 1994):
150
5 Flow Over Modified Surfaces
wavelength is longer than the hill height. This causes separation of the downwind
boundary layer of the hill, delivering a cavity zone, in the opposite direction to the
main flow. The drag force associated with the flow over a hill is maximum for the
resonance state (F r = 1). This force is lower if F r is lower than 1 and for the
separation boundary layer caused by natural waves of greater wavelength (F r > 1)
(Stull 1994).
5.5.2 Flow Under Neutral Conditions
The Froude number tends to infinity under neutral stability, and so cannot be used
for the characterization of the atmospheric flow. Over smooth topography, flow
separation and the formation of cavity areas are like those described above for
urban canopies. These processes are lighter and may even be absent (Taylor et al.
1987). Under neutrality, the streamlines are disturbed upstream and above the hill at
about threefold the hill height. Beyond this zone, the flow is not affected by the hill.
At the hilltop the streamlines converged, causing the wind to accelerate. Below the
downwind hill slope, strong winds cause a cavity area related to the separation of
the boundary layer and to the beginning of turbulent wakes. Their height is about
the same as the height of the hill, but increases in size along decreasing with
turbulence intensity, increasing downwards.
In general, airflow accelerates as it moves upstream over the top of the hills. The
acceleration factor A f , or fractional speedup is defined as the ratio Duðx; zÞ=u 0 ðzÞ,
where Duðx; zÞ is the difference between the mean horizontal streamwise velocity at
height z and u 0 ðzÞ. The u 0 ðzÞ is a reference velocity, at a downwind distance where
it is not influenced by the hill (Kaimal & Finnigan 1994). This A f factor decreases
with an increase in height (Fig. 5.12b) and varies between 1 and 2.5, depending on
hill shape, slope, and the ratio between the width and height. The magnitude of
speedup in hilltop is relevant for topics as diverse as wind power facilities or
estimation of wind load in buildings.
In the case of flow around a cone-shaped hill, rather than accelerating over the
top, the flow passes laterally around the surface (Fig. 5.12c) which remains
unchanged relatively to the flat surface (Rohatgi and Nelson 1994).
The highest rates of acceleration are seen around lightly sloped
three-dimensional hills (Arya 1988). The flow moving at oblique angles to the hills
is characterized by lateral vortices and a helical turbulent flow wake.
The mean hill width L 1/2 , is defined as the horizontal distance from the hill peak
to a point corresponding to half the peak height (Fig. 5.12a). For slightly sloping
hills, wind acceleration can be about twice the ratio of the hill height and L 1/2 . This
ratio is about 1.6 for isolated hills (Taylor and Teunissen 1987). For very slightly
sloping hills (height 100 m and L 1/2 about 250 m), wind acceleration above the top
will be about 60% compared to normal conditions.
Such data is relevant to the installation of wind turbines. The height at maximum
acceleration, Dz max , can be estimated as follows (Stull 1994):
150
5 Flow Over Modified Surfaces