Geoscience Reference
In-Depth Information
to the resistance. For neutral conditions the aerodynamic resistances are identical for
momentum and scalars (provided the observation levels are the same), and equal to:
()
z
z
u
2
1
ln
r
a
=
(3.25)
κ
*
This expression for the resistance follows directly from Eqs. (
3.23
) and (
3.24
) (there is
no new physics involved, only mathematics). Note that this resistance depends on the
two heights used (just as the diffusivity depends on height). The resistance decreases
with increasing friction velocity, and hence with increasing turbulence intensity. Fur-
thermore, the resistance increases when the distance between the two levels increases
(which is intuitive).
Question 3.16:
Check that under neutral conditions dimensional analysis leads to (
3.22
).
Question 3.17:
Equation (
3.25
) gives an expression for the aerodynamic resistance
under neutral conditions.
a) Given an observed value of the friction velocity
u
*
of 0.3 m s
-1
. Compute the resis-
tance between the levels 2.5 m and 8 m (include units in your answer!).
b) Show, using the expression in Eq. (
3.25
), what the total resistance will be if you
have two resistances in series (e.g., one between
z
1
and
z
2
and another between
z
2
and
z
3
).
Question 3.18:
Give the expressions similar to Eq. (
3.24
) but now for the latent heat
lux
L
v
E
) and for the mass lux of a scalar
x
(which has speciic concentration
q
x
).
Question 3.19:
Given the following observations of the mean wind speed at 2 and 4 m
height: 2.0 and 2.5 m s
-1
(assuming neutral conditions, see Eq. (
3.23
)):
a) Compute the friction velocity from the wind speed observations at 2 and 4 m.
b) Compute the wind speed at 10 m height.
3.5.5 Gradients and Proiles Under Conditions Affected by Buoyancy
Here we repeat the analysis made in
Section 3.5.4
(for the wind speed and tempera-
ture gradient only), but now for situations in which buoyancy
does
play a role (both
unstable and stable conditions). First we rewrite Eq. (
3.20
) to express the lux in terms
of the gradient. This gives:
τρ
κ
φ
uz
z
L
∂
∂
u
z
κ
uz
z
L
∂
∂
θ
=
c
*
,
Hc
=−
ρ
*
(3.26)
p
p
z
φ
m
h
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