Geoscience Reference
In-Depth Information
by pressure forces. Transfer for other entities is only by molecular diffusion. The
second complication (mentioned in Chapter 19, see Fig. 19.3) is that K Theory is
a poor representation of vertical diffusion inside vegetation canopies. But it is
often still used despite this. Fortunately the negative consequences of this do not
seem to be too severe.
Boundary layer exchange processes
During the 1960s and 1970s there was considerable interest in better quantifying
the aerodynamic behavior of components of natural vegetation inside canopies,
especially leaves. These studies focused on understanding differences in the
effectiveness with which different transferred entities (e.g., momentum, heat,
water vapor and carbon dioxide) are exchanged. Many studies were made inside
wind tunnels, often using artificial replicas of leaves and twigs. There is some
question as to how directly the results obtained in wind tunnels translate into
the real-world environment. Nonetheless, such studies contributed important
background understanding - helpful when considering the whole-canopy behavior
of vegetation stands. This section describes some of the more important results
obtained.
Boundary layers develop over smooth flat surfaces immersed in a moving fluid
such as air. Figure 21.1 illustrates a simple case in which air moving horizontally at
a fixed speed encounters a thin plate (equivalent to a flat leaf, perhaps). A layer of
air, the boundary layer, develops above the plate, which becomes deeper with dis-
tance from the leading edge. There is laminar (as opposed to turbulent) wind flow
inside this boundary layer, the wind speed varying from zero at the surface of the
plate to the speed of the incoming air flow at the edge of the boundary layer.
Momentum is transferred from the moving air through the boundary layer by
molecular diffusion, and the plate experiences a 'drag' force as a result.
The interaction between a moving fluid and obstructions in the fluid are
parameterized in terms of the Reynolds number defined in Chapter 17
(Equation 17.28). The velocity of air in a vegetation canopy is typically
∼
1.0 m s
-1
and a typical dimension of a leaf is
∼
0.05 m, giving a Reynolds Number of
order 10
4
.
When the primary exchange between the air flow and the flat plate is by molec-
ular diffusion through a boundary layer, the resulting sheer stress on the plate is
called '
skin friction
. Experimentally calibrated aerodynamic theory indicates that
the total transfer of momentum per unit area can be estimated from:
0.5
⎛⎞
=ρ
⎜
⎝⎠
U
t
0.66
U
(21.1)
a
l
where
U
is the speed of the air flow and l is the distance from the edge. If the net
exchange of momentum is expressed in terms of
R
M
sf
, the equivalent
