Geoscience Reference
In-Depth Information
Table 17.1
Physical meaning of the terms in the equations describing momentum
conservation for mean flow in a turbulent field.
∂
u
∂
u
∂
u
∂
u
1
∂
P
⎛
∂
(
uu
′′
)
∂
(
vu
′′
)
∂
(
′′
u
)
⎞
+
u
+
v
+
wfv
=
−
+
u
∇−
2
u
+
+
⎜
⎟
∂
t
∂
x
∂
y
∂
z
r
∂
x
∂
x
∂
y
∂
z
⎝
⎠
a
∂
v
∂
v
∂
v
∂
v
1
∂
P
⎛
∂
(
uv
′′
)
∂
(
vv
′′
)
∂
(
′′
v
)
⎞
+
u
+
v
+
w
= −
fu
−
+
u
∇−
2
v
+
+
⎜
⎟
∂
t
∂
x
∂
y
∂
z
ρ
∂
y
∂
x
∂
y
∂
z
⎝
⎠
a
∂
wwww
∂
∂
∂
1
∂
P
⎛
∂
(
uwvw
′′
)
∂
(
′′
)
∂
(
′′
w
)
⎞
+
u
+
v
+
w
= −
g
−
+
u
∇−
2
w
+
+
⎜
⎟
∂
t
∂
x
∂
y
∂
z
ρ
∂
z
∂
x
∂
y
∂
z
⎝
⎠
a
I
II
III
IV
V
VI
TERM I
Storage of mean momentum
TERM II
Advection of mean momentum
TERM III
Influence of Earth's rotation and gravity
TERM IV
Influence of mean pressure gradients
TERM V
Influence of viscous stress on mean motion (or divergence of molecular
momentum flux)
TERM VI
Influence of turbulent stress on mean motion (or divergence of turbulent momentum flux)
Table 17.2
Physical meaning of the terms in the equation describing moisture
conservation for mean flow in a turbulent field.
S
∂
q
∂
q
∂
q
∂
q
E
⎛
∂
(
uq
′′
)
∂
(
vq
′′
)
∂
(
′′
q
)
⎞
u
v
w
q
2
q
+
+
+
=
u
rr
+
+
∇−
+
+
⎜
⎟
q
∂
t
∂
x
∂
y
∂
z
⎝
∂
x
∂
y
∂
z
⎠
a
a
I II III IV V VI
TERM I
Storage of mean moisture
TERM II
Advection of mean moisture
TERM III
Mean 'body' source of moisture per unit volume
TERM IV
Mean creation of moisture as vapor per unit volume by evaporation of other water
phases
TERM V
Divergence of mean molecular moisture flux
TERM VI
Divergence of turbulent moisture flux
Neglecting molecular diffusion
The Reynolds number,
Re
, provides a measure of the ratio between the forces
giving turbulent diffusion in a fluid relative to those giving molecular diffusion.
For air, it is defined as the ratio:
