order of the equations to be solved and speeds up
the computation by a factor of 10 or more. The
finite size of the grid effectively introduces
numerical diffusion that simulates many of the
same mean flow features developed using the
more complex turbulence closures.
Another simplification to speed up the computation of the mean velocity field is to represent the
effects of the individual buildings as a distributed
force acting on the flow (or source/sink distribution) and thereby only approximately representing
the shape of the building [64]. In most FCM
calculations, considerable computational resource
and time is spent on exactly representing the
building shape, while at the same time making
considerable approximations in the flow.
There are at present no general FAMs that are
capable of calculating the detailed flow around
any isolated building or group of buildings, or
even calculating those broad features of the flow
needed for modelling dispersion close to the
building. The main reason is that the unsteady
separated shear layers that control the flow are of
much smaller scale than the building. This means
that the recirculating flow region, which greatly
affects the magnitude and timescale of concentration fluctuation, is not only highly unsteady but
also very sensitive to the effects of nearby buildings. Nevertheless, the main features of the mean
flow patterns and typical magnitudes of the mean
and fluctuating velocity have been classified and
partially quantified for many types of buildings
and groupings. Therefore, although no practical
FAM for the mean flow is available at present,
these features of the flow field are now well
enough known to derive useful quantitative
FAMs for the dispersion. For example, when
buildings are far enough apart that their nearflow fields and their wakes are approximately
independent, the wakes can be approximated as
a perturbation to the approach flow, a theory by
Counihan et al., 1974 [21] that is used in the
“Buildings” module in ADMS [67]. The same
model can be used approximately with linear
superposition when buildings are separated by at
least 3H, where H is their height. As the ratio of
breadth to height, b/H, increases from 1.0 to
10, this minimum separation distance d min
increases linearly to about 10 H (Fig. 3a(i)).
When d is less than d min (Fig. 3a(ii)), it is found
that the recirculating regions of the wakes of the
upwind buildings are elongated and extend to the
nearest downwind building [65]. For buildings
designed in rows nearly parallel with the wind
direction, the flow structure consists of turbulent
recirculating regions in the spaces downwind of the
buildings and relatively high-speed streams in the
open streets between the buildings [28]. Describing
the flow structure in this way provides the basis for
FAM for dispersion calculations.
By contrast, when the buildings are placed in a
staggered pattern relative to the wind direction,
the wakes tend to disappear and the mean flow
between the buildings consists largely of unidirectional bifurcating patterns of diverging and
converging streamlines, with small regions of
recirculating flow. Such flow can be computed
by fast potential flow methods [28], which are
even faster if the shape of the layout of the buildings is approximated [64].
When the buildings are long enough and close
enough (i.e., categories (i), (ii), and (iii) of
Table 3) and the wind is at any angle, or if they
are situated in rows and the wind is at a small
glancing angle to the row (Fig. 3a(ii)), then the
characteristic canyon flows are formed in the
streets between the buildings. When the buildings
either side of the street are of comparable height, a
strong feature of the helical canyon flow is that it
does not extend above the buildings. Therefore
the appropriate FAM for these flows is to assume a
canyon flow below the building level and a rough
wall boundary layer flow above it [23].
The final consideration is of the air flow in
typical courtyards and “squares” connected to
adjoining streets (Fig. 3c). Simulations confirm
that these are regions where fluid trajectories are
well mixed. This provides a basis for constructing
FAMs for dispersion in these regions using semianalytical diffusivity models.
Examples of Output of Modelling
Calculations
A series of examples of recent model calculations
showing the impact of buildings on flow are now
reported. The cases considered are a single
Urban Air Quality: Meteorological Processes
179
the computation by a factor of 10 or more. The
finite size of the grid effectively introduces
numerical diffusion that simulates many of the
same mean flow features developed using the
more complex turbulence closures.
Another simplification to speed up the computation of the mean velocity field is to represent the
effects of the individual buildings as a distributed
force acting on the flow (or source/sink distribution) and thereby only approximately representing
the shape of the building [64]. In most FCM
calculations, considerable computational resource
and time is spent on exactly representing the
building shape, while at the same time making
considerable approximations in the flow.
There are at present no general FAMs that are
capable of calculating the detailed flow around
any isolated building or group of buildings, or
even calculating those broad features of the flow
needed for modelling dispersion close to the
building. The main reason is that the unsteady
separated shear layers that control the flow are of
much smaller scale than the building. This means
that the recirculating flow region, which greatly
affects the magnitude and timescale of concentration fluctuation, is not only highly unsteady but
also very sensitive to the effects of nearby buildings. Nevertheless, the main features of the mean
flow patterns and typical magnitudes of the mean
and fluctuating velocity have been classified and
partially quantified for many types of buildings
and groupings. Therefore, although no practical
FAM for the mean flow is available at present,
these features of the flow field are now well
enough known to derive useful quantitative
FAMs for the dispersion. For example, when
buildings are far enough apart that their nearflow fields and their wakes are approximately
independent, the wakes can be approximated as
a perturbation to the approach flow, a theory by
Counihan et al., 1974 [21] that is used in the
“Buildings” module in ADMS [67]. The same
model can be used approximately with linear
superposition when buildings are separated by at
least 3H, where H is their height. As the ratio of
breadth to height, b/H, increases from 1.0 to
10, this minimum separation distance d min
increases linearly to about 10 H (Fig. 3a(i)).
When d is less than d min (Fig. 3a(ii)), it is found
that the recirculating regions of the wakes of the
upwind buildings are elongated and extend to the
nearest downwind building [65]. For buildings
designed in rows nearly parallel with the wind
direction, the flow structure consists of turbulent
recirculating regions in the spaces downwind of the
buildings and relatively high-speed streams in the
open streets between the buildings [28]. Describing
the flow structure in this way provides the basis for
FAM for dispersion calculations.
By contrast, when the buildings are placed in a
staggered pattern relative to the wind direction,
the wakes tend to disappear and the mean flow
between the buildings consists largely of unidirectional bifurcating patterns of diverging and
converging streamlines, with small regions of
recirculating flow. Such flow can be computed
by fast potential flow methods [28], which are
even faster if the shape of the layout of the buildings is approximated [64].
When the buildings are long enough and close
enough (i.e., categories (i), (ii), and (iii) of
Table 3) and the wind is at any angle, or if they
are situated in rows and the wind is at a small
glancing angle to the row (Fig. 3a(ii)), then the
characteristic canyon flows are formed in the
streets between the buildings. When the buildings
either side of the street are of comparable height, a
strong feature of the helical canyon flow is that it
does not extend above the buildings. Therefore
the appropriate FAM for these flows is to assume a
canyon flow below the building level and a rough
wall boundary layer flow above it [23].
The final consideration is of the air flow in
typical courtyards and “squares” connected to
adjoining streets (Fig. 3c). Simulations confirm
that these are regions where fluid trajectories are
well mixed. This provides a basis for constructing
FAMs for dispersion in these regions using semianalytical diffusivity models.
Examples of Output of Modelling
Calculations
A series of examples of recent model calculations
showing the impact of buildings on flow are now
reported. The cases considered are a single
Urban Air Quality: Meteorological Processes
179