Geoscience Reference
In-Depth Information
Table 16.1
The suite of equations that describe the evolution of atmospheric variables in
the atmosphere.
Ideal Gas Law:
P
=
r
a
R
d
T
v
Conservation of mass:
In general
In the ABL
∂∂∂
++ =
∂∂ ∂
uvw
x
∂
ρ
⎛
∂∂∂
uvw
⎞
0
a
=−
ρ
+
+
⎜
⎟
a
y
z
∂
t
⎝
∂
x
∂
y
∂
z
⎠
Conservation of momentum:
du
∂
u
∂
u
∂
u
∂
u
1
∂
P
⎛
∂
2
u
∂
2
u
∂
2
u
⎞
=+ + +
u
v
w fv
= −
+
υ
+ +
⎜
⎟
dt
t
x
y
z
x
x
2
y
2
z
2
∂
∂
∂
∂
ρ
∂
⎝
∂
∂
∂
⎠
a
dv
∂
v
∂
v
∂
v
∂
v
1
∂
P
⎛
∂
2
v
∂
2
v
∂
2
v
⎞
=+ + +
u
v
w
=−−
fu
+
υ
+ +
⎜
⎟
dt
t
x
y
z
y
x
2
y
2
z
2
∂
∂
∂
∂
ρ
∂
⎝
∂
∂
∂
⎠
a
dwwww w
∂
∂
∂
∂
1
∂
P
⎛
∂
2
www
∂
2
∂
2
⎞
=+ + +
u
v
w g
=−−
+
υ
+ +
⎜
⎟
dt
t
x
y
z
z
x
2
y
2
z
2
∂
∂
∂
∂
ρ
∂
⎝
∂
∂
∂
⎠
a
Conservation of moisture:
S
∂
q
E
vq
.
2
q
+
q
+
v
+∇= ∇
υ
(vapor)
q
∂
t
ρρ
a
a
l
l
S
∂
q
E
l
2
l
q
+∇ = ∇
vq
.
υ
q
+
−
v
(liquid/solid)
q
∂
t
ρρ
a
a
Conservation of energy:
∂
θ
1
λ
E
+∇= ∇ −
v
.
θυ θ
ρ
2
∇ −
R
v
θ
n
∂
t
c
ρ
c
ap
ap
Conservation of a scalar quantity:
∂
c
+∇= ∇+
vc
.
υ
2
cS
c
c
∂
t
molecular transfer while the second represents all possible sources or sinks of
the quantity (which might include chemical reactions that occur at some level
in the atmosphere, as in the case of ozone). Consequently, the general conser-
vation for such scalar quantities (for conciseness here in vector format) takes
the form:
∂
c
vc cS
t
.
2
(16.50)
+∇=υ∇+
q
c
∂
