Geoscience Reference
In-Depth Information
(a)
1.0
0.5
0
0.001
0.01
0.1
1
10
100
1000
(b)
0.4
Buoyant
production
Shear
production
0.2
0
−
0.2
Energy transfer between
eddy frequencies
Dissipation
−
0.4
0.001
0.01
0.1
1
10
100
1000
TKE in large eddies produced
by both buoyancy and shear
TKE dissipated small
eddies by friction
Frequency of turbulent eddy
Figure 18.8
(a) Typical example of the relative strength of the contributions to TKE at different frequencies; (b) typical
change in the relative magnitude of the production and destruction terms in the prognostic equation for TKE and the
energy transfer (between frequencies) as a function of eddy frequency.
variance in vertical wind speed. For moisture fluctuations the resulting equation
has the form:
()
2
⎡
⎤
q
q
q
∂
q
′
2
2
2
⎡
⎤
∂
()
q
′
∂
()
q
′
∂
()
q
′
∂
∂
∂
+ u.
⎢
+v.
+w.
⎥
=
−′ ′
2
q u .
+q v .
′ ′
+q w .
′
′
⎢
⎥
∂
t
∂
x
∂
y
∂
z
∂
x
∂
y
∂
z
⎢
⎥
⎢
⎥
⎣
⎦
⎣
⎦
I II
III
(18.19)
⎡
⎤
⎡
⎤
2
2
2
2
2
2
⎛
⎞
∂
u
′
()
q
′
∂
v
′
()
q
′
∂
w
′
()
q
′
⎛
∂
q
′
⎞
∂
q
′
⎛
∂
q
′
⎞
⎢
⎥
+
−
⎢
+
⎥
−
2
ν
+
+
⎜
⎟
⎜
⎟
⎜
⎟
∂
x
∂
y
∂
z
⎢
⎝
∂
x
⎠
∂
y
⎝
∂
z
⎠
⎥
⎝
⎠
⎢
⎥
⎣
⎦
⎣
⎦
IV
V
