Geoscience Reference
In-Depth Information
z
Fig. 2.5
Sketch illustrating a small fluid
parcel, which rises a small distance
w
δ
t
, to a
le
vel, where the mean
humidity
q
is lower by an amount
q
than at its original position.
′
q
′ δ
w
t
Mean specific humidity,
⎯
q
moving in all directions and the transport rate by all of them, i.e. the vertical transport
of water vapor mass per unit horizontal area and per unit time is on average as indicated
in Equation (2.29).
Similar expressions can be written for the fluxes of other properties or admixtures of
th
e flow. The vertical flux component of horizontal momentum, with mean concentration
u
,is
F
m
z
=
ρw
u
(2.30)
and that of sensible heat, with mean concentration
c
p
θ
, can be written as
F
h
z
=
ρ
c
p
w
θ
(2.31)
Under steady conditions in the lowest few meters of the air above a uniform surface,
on account of continuity the inflow rate equals the outflow rate, which means that these
vertical fluxes must be constant with elevation. Hence the water vapor flux
in Eq
uation
(2.29) is in fact equal to the rate of evaporation
E
from the surface, or
F
v
z
=
ρw
q
0
≡
E
,
in which the 0 subscript denotes the value near the surface. In the case of momentum,
there is a sink at the surface in the form of a shear stress, so that close to the surface it
can also be assumed that
F
m
z
≡−
τ
=−
τ
0
, in which
τ
0
is the shear stress at the surface.
Similarly t
he fl
ux in Equation (2.31) equals the sensible heat flux
H
at the surface, or
F
h
z
=
ρ
c
p
w
θ
0
≡
H
. For convenience of notation, the surface shear stress, which is
