Geoscience Reference
In-Depth Information
now reached the stage of writing equations derived from turbulence theory
that  can be used to calculate fluxes from mean variables and the aerodynamic
properties of natural surfaces, it is now appropriate to recast these equations
back into the natural units in which they are normally applied.
As described in Table 15.3 and associated text, the process of returning from
kinematic fluxes to actual fluxes involves (for most fluxes) substituting the true
flux divided by the density of moist air for the kinematic version of fluxes in
equations derived from turbulence theory. However, in the case of sensible heat
flux, the true sensible heat flux divided by the product of the density of moist air
with the specific heat of air must be substituted for the kinematic sensible heat
flux. Taking sensible heat flux as an example, this means that the definition of q *
given in Equation (20.6) is re-expressed in terms of the true flux of sensible heat,
H , and becomes:
H
cu
(20.16)
q
=
*
r
*
ap
When this definition of q * is substituted into Equation (20.5), it can be rearranged
to give:
kz du
(
)
∂θ
*
(20.17)
v
2
Hc
=−
r
(W m
)
p
z
φ
H
Similarly, rewriting the definition of q * in terms of the actual moisture flux, E , and
substituting this into Equation (20.8) and rearranging gives:
kz du q
(
)
(20.18)
*
−−
2
1
E
=−
r
(kg m
s
)
z
φ
V
Moisture flux is often expressed in terms of the equivalent flux of latent heat, in
which case this last equation becomes:
kz du q
(
)
*
(20.19)
2
l
E
=−
rl
(W m
)
z
f
V
and in practice, when describing near-surface energy exchange, it has become
more common to express latent heat flux in terms of the gradient of vapor pressure
rather than the gradient of specific humidity, and to use the alternative equation:
r
c kz du e
(
)
(20.20)
*
p
E
2
l
=−
(W m
)
g
f
z
V
where g
) is the psychrometric constant introduced in Equation
(2.25). The equivalent equation describing the eddy diffusion of momentum flux
is obtained by multiplying both the numerator and denominator on the right hand
=
( c p P )/(0.622
λ
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