Fundamentals Of Geophysical Fluid Dynamics Part 1 pdf
Fundamentals Of Geophysical Fluid Dynamics Part 1 pdf
... scale, L, is sufficiently small,
2 .1 Fluid Dynamics 29
2 .1. 4 Energy Conservation
The principle of energy conservation is a basic law of physics, but in
the context of fluid dynamics it is derived from ... vertical scale of the motion is small in the sense of
˜
H
κ
1 − κ
H
0
≈ 12 km .
Even for troposphere-filling motions (with a vertical extent ∼ 10 km),
this approxim...
Fundamentals Of Geophysical Fluid Dynamics Part 7 pdf
... g/kg
Height AGL, km
8 9 10 11 12 13 14 15 16 17
0
0.5
1
1.5
2
2.5
3
Reflectivity, PBL height, and cloud base
Time (CST)
Height AGL, km
Day 266 19 95
Fig. 6 .1. Example of reflectivities (bottom) ... without loss of generality, been presumed to
6 .1 Planetary Boundary Layer 215
5 10 15 20
0
1
2
3
0900
10 30
12 00
13 30
Virtual potential temperature, C
Height AGL, km
0 5...
Fundamentals Of Geophysical Fluid Dynamics Part 2 ppt
... hydrostatic,
∂φ
∂z
= −g
ρ
ρ
o
= −g (1 −αθ) , (2 .10 4)
expressed here as a notational hybrid of (2.33), (2.58) and (2.80) with
the simple equation of state,
ρ/ρ
o
= 1 −αθ .
Combining (2 .10 3)-(2 .10 4) yields
f
∂v
g
∂z
= ... asymmetrically located at (±
√
3, 1) ,
(1, 1) ; (c) four vortices symmetrically located at (±
√
3, 1) , (0, 2), (0, 0); and
(d) four vortices asymmetrically loc...
Fundamentals Of Geophysical Fluid Dynamics Part 3 potx
... mode
even mode
odd mode
0
1. 0
2.0
0 1. 0
2.0
1. 0
0.5
0 .15
0 .10
0.05
c
r
kL
0
Fig. 3 .12 . Eigenvalues for the barotropic instability of the Bickley Jet: (a) the
real part of the zonal phase speed, ... (3 .11 4)
with
KE(k) =
1
2
k
2
S, Ens(k) =
1
2
k
4
S = k
2
KE(k) . (3 .11 5)
The latter relations are a consequence of the spatial gradient of ψ having
a Fourier transfo...
Fundamentals Of Geophysical Fluid Dynamics Part 4 pptx
... speed.
Thus, the dynamics of a Kelvin wave is a hybrid combination of the
influences of rotation and stratification.
The ocean is full of Kelvin waves near the coasts, generated as part
of the response ... (4.42)
Deep internal gravity wave speeds are typically O (10
2
) m s
1
in the
4 .1 Rotating Shallow-Water Equations 12 3
t∆
1
ζf
1
+
ζ
2
f
2
+
h
1
h
2
Fig. 4.5. Vorte...
Fundamentals Of Geophysical Fluid Dynamics Part 5 docx
... −
δp
1
− δp
2
g∆ρ
= −δh
1
from (5 .1) . Hence, using the geostrophic approximation and the linear
dependence of w within the layers,
∂w
1
∂z
=
w(H) −w
I
h
1
≈ −
w
I
H
1
≈
f
0
g
I
H
1
D
Dt
g ,1
(ψ
1
− ... (5 .11 )
Similarly,
∂w
2
∂z
≈ −
f
0
g
I
H
2
D
Dt
g,2
(ψ
1
− ψ
2
) . (5 .12 )
There is no discontinuity associated with which layer’s D
t
appears in
(5 .11 )-(5 .12 ) si...
Fundamentals Of Geophysical Fluid Dynamics Part 6 ppt
... q
T
n+.5
(y) [K]
6
6
6
m]y [10
m]
m]y [10
y [10
n
1
](y) [m s
v
a,n
(y) [10 m s
1
]
(y) [10 m ] s
12
1
]
[10 s ]
1
(y) [10 m s
5
−3
−6 −7
0
1
2
0
1
2
0
1
2
0
10
10
Fig. 5 .14 . Time-mean meridional ... Jet Dynamics
3
τ
s
x
=
n =1
n=3
stress ]
−2
s
2
[10 m
− 4
stress ]
−2
s
2
[10 m
− 4
y [10 ]m
6
y [10 ]m
6
u
3
H
1
∂
y
R
1
∂
y
R
3
3
ε
bot
−D
1. 5
D
2.5
H
−...
Fundamentals Of Geophysical Fluid Dynamics Part 8 pptx
... 10
11
m
1
s
1
,
τ
0
= 0 .1 N m
−2
= ρ
o
× 10
−4
m
2
s
−2
, h
ek, top
= 10 0 m ,
=⇒ v
i
∼ A = 10
−3
m s
1
.
=⇒ ν
e
= 0.5 m
2
s
1
, v
ek, top
= 10
−2
m s
1
, and E = 10
−4
.
=⇒ ∆x
b
∼ D = 5 × 10
4
m and
D
L
x
= ... outside of the boundary layer.
In the interior the flow is barotropic. Therefore, the depth-averaged
256 Boundary-Layer and Wind-Gyre Dynamics
f
0
= 10...
Fundamentals Of Geophysical Fluid Dynamics Part 9 pot
... 45, 49, 62, 71, 11 5,
11 6, 11 9, 12 8, 12 9, 13 1, 13 3, 17 3,
17 9, 18 9, 19 0, 207, 214 , 224, 242,
258, 274
streakline, 23
streamfunction, 34, 61, 67, 17 2, 244,
247, 264
streamline, 22, 61, 64, 264
stretching ... coordinates, 51, 266
Primitive Equations, 54, 11 6, 11 7, 15 4,
16 8, 17 1, 17 2
prognostic variable, 41, 75
pycnocline, 11 6, 11 9, 16 2, 214 , 224
quasi-p...