Geoscience Reference
In-Depth Information
Table 15.3
The interrelationship between true and kinematic fluxes and their respective units.
Actual flux
Units of
actual flux
Measurable
variable
Relationship of kinematic
flux to actual flux
Units of kinematic
flux
M
Mass
kg
air
m
−2
s
−1
Velocity
M
=
m s
−1
k
ρ
a
H
Sensible heat
J m
−2
s
−1
Potential
temperature
H
=
K m s
−1
k
c
ρ
pa
τ
Momentum
kg m
−1
s
−2
Velocity (in
prescribed direction)
m
2
s
−2
τ
=
k
ρ
E
Moisture
kg
water
m
−2
s
−1
Specific humidity
kg
water
kg
air
−1
m s
−1
E
=
k
ρ
a
C
Constituent
kg
constit
m
−2
s
−1
Relative density of
constituent
C
=
kg
constit
kg
air
−1
m s
−1
k
ρ
a
Advective and turbulent fluxes
As just described, the kinematic version of the fluxes of mass, sensible heat,
momentum and moisture and minority constituent are given by taking the time-
average of the product of a relevant atmospheric variable with the velocity
component in the direction of interest. Taking as an example the kinematic
sensible heat moving in the direction of the Z axis, the kinematic vertical flux of
sensible heat flux is the time-average product of
q
v
and
w
into the mean and fluctuating components defined over the averaging period, the
total sensible heat flux is therefore calculated from:
q
v
with
w
. Separating
(15.22)
H
=
(
q
w
)
=
(
q
+
q
′
)(
w w
+
′
)
k
v
v
v
c
p
)
because it describes the
kinematic flux
of sensible heat, and it also allows the
possibility of a sensible heat flux associated with the mean vertical flow of air at
mean air temperature. By analogy with Equation (15.8), Equation (15.22) becomes:
This last equation differs from Equation (7.8) in that it no longer includes (
r
(15.23)
(
q
w
)
=
(
q
)
w
+
(
q
′
w
′
)
v
v
v
The first term in Equation (15.23) has dimensions of kinematic sensible heat flux and
describes the mean flow, in this case of thermal energy. It is called the
Advective Flux
or
Mean Flux
and it calculates the possible vertical heat flow that might occur via
transfers that happen on the low frequency side of the spectral gap (Fig. 15.3) if there
were a finite vertical wind speed over the time period for which averaging is made.
