surrounds the obstacle horizontally without vertical flow (Fig. 5.11). Upwind of the
hill, some blocking and atmospheric stagnation can also occur. The flow blocked by
topography has a preponderant influence on the local microclimate and on the
dispersion of pollutants emitted upwind (Arya 1988).
For winds with higher velocity, or lower thermal stability (F r about 0.4), some
air rises the hill (Fig. 5.11), while airflow at lower levels diverge moving around
obstacles symmetrically and horizontally. It is, therefore, possible to distinguish
between streamlines of airflow around topography and of rising airflow (Snyder
et al. 1985). The height H s , of this separation streamline, can be estimated assuming
that the kinetic energy of a fluid layer, following a streamline, is equal to the
potential energy of the stratification. The overall equation of the process is given by
(Sheppard 1956)
1
2
qu
2
o H s
ð Þ ¼ g
Z H h
H s
H h À z
ð
Þ À
@q
@z
@z
ð5:11Þ
where H h is the height of the hill. For the case of stratified flow, with a constant
density gradient, the height H s is given by (Hunt and Snyder 1980)
H s ¼ H h 1 À F r
ð
Þ
ð5:12Þ
The wavelength of the flow over the hill is much smaller than its height, and thus
induces the formation of gravity waves, downwind from the hill, which is separated
from the surface of the topographic obstacle. This flow separation will occur above
the air that does not oscillate and surrounds the hill. The fraction of the air column,
with height equal to the hill height, flowing over the top of the hill, is of the order of
magnitude of the Froude number (Stull 1994)
Fr ¼
z h0
z hill
ð5:13Þ
where z ho is the height of the air column rising above the hill that separates
downwind from the obstacle surface and z hill is the total height of the hill.
Experimental results bear out the separation streamline principle (Snyder et al.
1985). Regardless of the thermal stratification, the angle of the flow orientation
relative to a hill and the upwind hill slope are variables that can also be decisive in
allowing the air to rise or surround the topographical obstacle (Arya 1988).
Figure. 5.11 represents the effects of thermal stability on the flow on an isolated
hill. For a unit Froude number, the stability is weaker, and the winds are stronger,
so that the natural wavelength matches the height of the hill. Large amplitude
gravity waves or mountain waves are generated by this natural resonance with the
possibility of recirculation near the ground close to the wave crests. In this situation,
surface air stagnates at periodic intervals downwind of the hill, and reverse flow can
148
5 Flow Over Modified Surfaces
hill, some blocking and atmospheric stagnation can also occur. The flow blocked by
topography has a preponderant influence on the local microclimate and on the
dispersion of pollutants emitted upwind (Arya 1988).
For winds with higher velocity, or lower thermal stability (F r about 0.4), some
air rises the hill (Fig. 5.11), while airflow at lower levels diverge moving around
obstacles symmetrically and horizontally. It is, therefore, possible to distinguish
between streamlines of airflow around topography and of rising airflow (Snyder
et al. 1985). The height H s , of this separation streamline, can be estimated assuming
that the kinetic energy of a fluid layer, following a streamline, is equal to the
potential energy of the stratification. The overall equation of the process is given by
(Sheppard 1956)
1
2
qu
2
o H s
ð Þ ¼ g
Z H h
H s
H h À z
ð
Þ À
@q
@z
@z
ð5:11Þ
where H h is the height of the hill. For the case of stratified flow, with a constant
density gradient, the height H s is given by (Hunt and Snyder 1980)
H s ¼ H h 1 À F r
ð
Þ
ð5:12Þ
The wavelength of the flow over the hill is much smaller than its height, and thus
induces the formation of gravity waves, downwind from the hill, which is separated
from the surface of the topographic obstacle. This flow separation will occur above
the air that does not oscillate and surrounds the hill. The fraction of the air column,
with height equal to the hill height, flowing over the top of the hill, is of the order of
magnitude of the Froude number (Stull 1994)
Fr ¼
z h0
z hill
ð5:13Þ
where z ho is the height of the air column rising above the hill that separates
downwind from the obstacle surface and z hill is the total height of the hill.
Experimental results bear out the separation streamline principle (Snyder et al.
1985). Regardless of the thermal stratification, the angle of the flow orientation
relative to a hill and the upwind hill slope are variables that can also be decisive in
allowing the air to rise or surround the topographical obstacle (Arya 1988).
Figure. 5.11 represents the effects of thermal stability on the flow on an isolated
hill. For a unit Froude number, the stability is weaker, and the winds are stronger,
so that the natural wavelength matches the height of the hill. Large amplitude
gravity waves or mountain waves are generated by this natural resonance with the
possibility of recirculation near the ground close to the wave crests. In this situation,
surface air stagnates at periodic intervals downwind of the hill, and reverse flow can
148
5 Flow Over Modified Surfaces