Geoscience Reference
In-Depth Information
2.4
THE ATMOSPHERIC BOUNDARY LAYER
2.4.1
Quasi-homogeneous conditions
In the atmosphere the largest changes in wind velocity, temperature and humidity are
usually found in the vertical direction and in a distinct region near the surface. In contrast,
horizontal changes are relatively mild, and tend to occur over distances of the order of
tens of kilometers. For this reason the air near the surface may be regarded as a boundary
layer, a concept set forth by Prandtl (1904) for momentum transport in the neighborhood
of a solid wall. The atmospheric boundary layer (or ABL) can be defined as the lower part
of the atmosphere, where the nature and properties of the surface affect the turbulence
directly. Accordingly, the horizontal scales of most atmospheric flow phenomena of
interest in hydrology are much larger than the vertical, so that the horizontal gradients
are usually small compared to the vertical gradients, and the vertical velocities are small
relative to the horizontal velocities. Thus, many problems can be solved by simply
assuming that
∂
∂
∂
∂
x
,
=
w
=
0
and
0
(2.28)
y
In addition, since
x
is the direction of the mean wind velocity near the ground, the mean
velocity in the lateral
y
-direction can also be discarded, or
0. Strictly speaking (2.28)
is valid only when the surface is perfectly homogeneous or uniform. Such conditions
are rare, and the properties of most natural landsurfaces are spatially quite variable;
fortunately, in many situations of interest they can be considered to be at least statistically
homogeneous (see, for example, Brutsaert, 1998), and the assumptions of (2.28) can still
be used to describe the flow.
More generally (2.28) is tantamount to assuming that, as the air moves parallel to
a homogeneous surface, on average (in the turbulence sense) the concentration of any
property or admixture advected by the air changes only in the vertical and remains
constant in the horizontal direction. The fact that the mean concentrations change only
vertically is evidence that there is a source or a sink of the admixture at the surface, and
thus the only turbulent fluxes of consequence are the vertical c
o
mponents. In the case
of humidity with mean concentration (per unit mass of bulk air)
q
, Equations (2.26) are
thus effectively reduced to
v
=
F
v
z
=
ρ w
q
(2.29)
in which henceforth the overbar on
F
v
z
is omitted for convenience of notation.
While mathematically Equations (2.26) and (2.29) are unambiguous, a more intu-
itive sense of their physical significance can be obtained by considering the mechanism
sketched in Figure 2.5. A particle of air, which undergoes a vertical velocity fluctuation
w
, travels a distance
w
δ
t
during a time interval
δ
t
. After that air parcel has risen a
w
δ
small distance
t
from a level, where the mean specific humidity is
q
, it has a specific
humidity which is
q
larger than the mean of its new environment; thus the rate (distance
per unit time) at which this particular parcel transports absolute humidity upward is
(
q
w
) times its volume. There are many such parcels - or eddies - in turbulent flow
ρ
