Geoscience Reference
In-Depth Information
This situation is still stable. However, if the particle is made to rise further, and con-
tinues to cool down, it may reach the level
z
C
, where condensation takes place; above
the condensation level
z
C
it will change its temperature at the saturated adiabatic lapse
rate. If the rise continues, eventually above the level
z
F
the temperature of the particle
will exceed that of the surroundings; the rising air is now lighter than its surroundings,
and an unstable situation has been established. The air, which was originally forced to
rise, will now take off by free convection and continue to rise without any outside agent.
The height
z
F
is the free convection level. Thus whether or not a vertical displacement
results in instability depends largely on the moisture content of the atmosphere. In a
moist atmosphere the condensation level is low, and relatively small vertical displace-
ments readily produce unstable conditions. In a dry atmosphere, the level
z
C
is higher,
and the atmosphere is more likely to remain stable, even with relatively large vertical
displacements.
2.3
TURBULENT TRANSPORT OF WATER VAPOR
The flow of the atmosphere is almost invariably turbulent. In a turbulent flow molecular
diffusion can usually be neglected, and water vapor is moved from one place to another
by advective transport, that is, by being linked to the motions of the air that contains
it. One exception, when molecular diffusion may be of some consequence, occurs near
a wall where the no slip condition reduces the velocity of the moving air to zero and
the turbulence is largely suppressed. Thus in turbulent air flow, the specific mass flux of
water vapor is given by
F
v
=
ρ
v
v
=
ρ
q
v
(2.25)
where
v
is the velocity of the air,
ρ
v
is the water vapor density, and
q
is the specific humid-
ity. The variables
F
v
=
are both vectors, with
x
denoting the direction of the mean wind near the ground and
z
the vertical.
Note that the transport described by Equation (2.25) can also be referred to as
con-
vection
in fluid mechanics. However, this usage may lead to some confusion because,
especially in the atmospheric sciences, convection is commonly reserved to describe
transport involving gravity effects, resulting from unstable density stratification. To avoid
such confusion in this regard, in this topic any transport that is linked to the motion of
the fluid is called
advection
.
i
F
v
x
+
j
F
v
y
+
k
F
v
z
and
v
=
i
u
+
j
v
+
k
w
Turbulent flux of water vapor
In turbulent flow the detailed description of the velocity field and also the temperature,
the content of water vapor, or other admixtures of the air, at any given point in time
and space, is practically impossible and it can only be accomplished in a statistical
sense. The simplest and probably most important statistic is the mean. Accordingly,
ever since Reynolds introduced the idea, it has been common practice in the analysis
of turbulent flow phenomena to dec
omp
ose the relevant variables into a mean and a
turbulent fluctuation, namely
F
v
x
=
F
v
x
,...,
u
,...,
q
, etc.
F
v
x
+
u
=
u
+
q
=
q
+
