Geoscience Reference
In-Depth Information
millimeters), molecular flow remains important - the consequences of this are
discussed in Chapter 21.
All equations describing mean flow in a turbulent field include two flux
divergence terms, one describing transfer by molecular transfer and the other
turbulent transfer. In Equation (17.25), for example, these terms are respectively:
2
2
2
www uw vwww
(
′′
)
(
′′
)
(
′′
)
2
(17.29)
u
w
or
u
+
+
and
+
+
x
2
y
2
z
2
x
y
z
Because transfer by turbulent transfer is much more efficient than that by molecular
transfer in the ABL, it is acceptable at this stage to neglect the term describing
divergence of molecular transfer in each conservation equation. Table 17.5
Table 17.5 The suite of equations that describe the evolution of mean atmospheric flow
in the ABL including the effect of turbulent flux divergence.
Ideal Gas Law:
PR T
=
ρ
dav
Conservation of Mass:
In general
In the ABL
∂∂∂
∂∂ ∂
uv
w
∂ρ
∂∂∂
uv
w
++ =
0
a
=−
ρ
+
+
a
x
y
z
t
x
y
z
Conservation of Momentum:
u
u
u
u
(
uu
′′
)
(
vu
′′
)
(
wu
′′
)
+
u
+
v
+
w fV
= −
(
v
)
+
+
g
t
x
y
z
x
y
z
v
v
v
v
(
uv
′′
)
(
vv
′′
)
(
wv
′′
)
+
u
+
v
+
w fU
= −
(
u
)
+
+
g
t
x
y
z
x
y
z
wwww
(
uwvw
′′
)
(
′′
)
(
′′
w
)
+
u
+
v
+
w g
= −
+
+
t
x
y
z
x
y
z
Conservation of Moisture:
SE
+
q
q
q
q
(
uq
′′
)
(
vq
′′
)
(
′′
q
)
q
+
u
+
v
+
w
=
+
+
t
x
y
z
x
y
z
ρ
a
Conservation of Energy:
q
θ θ θ
∇ +
RE
∂θ∂θ∂θ
(
u
′′
)
(
v
′′
)
(
w
′′
)
+
u
+
v
+
w
= −
n
+
+
t
x
y
z
x
y
z
c
ρ
ap
Conservation of a Scalar Quantity:
c
c
c
c
(
uc
′′
)
(
vc
′′
)
(
′′
c
)
+
u
+
v
+
wS
=
+
+
c
t
x
y
z
x
y
z
 
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