Met Ss04 Chapter 4
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Transcript of Met Ss04 Chapter 4
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IV/1
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IV/2
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IV/3
Dynamics: Introduction
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Pressure gradient force
ii
dvF F m
dt= =
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IV/5
Pressure gradient force
left
right
F p dy dz
pF p dx dy dz
x
=
= +
xp left right
p pF F F dx dy dz dV
x x
= + = =
1
m
p dV p
x dm x
=
m mV=
1 1p
m m
f p grad p
= =
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IV/6
Pressure gradient force
1 1p
m m
f p grad p
= =
p
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IV/7
Thermal circulation
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IV/8
Thermal circulation
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IV/9
baroclinity and thermal circulation
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IV/10
Gravity force
gF m g=
gf g g k= =
0
1 ( , )' ( , ')
h
ho o
g hz dh g h h
g g
==
( , )
0
0
= =
= = =
o
g z h
o
g z g h h
f
g z
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IV/11
Friction
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Coriolis force
cF
*
cF
2 2 /dv
m m r m v rdt
= =
* 0c cF F+ =
2 /T=
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IV/13
Coriolis force
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IV/14
Coriolis force
2 sin= = a v f v
2 sin Coriolis parameter f
( )cos cos dcosd
+
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Coriolis force
( ) ( )2advdv
v rdt dt
=
( )2Cf v=
( ) 2r r =
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IV/16
Coriolis force
( )2Cf v=
( )
( )( )
( ) ( )
0
2 2 cos
sin
2 sin cos
2 sin2 cos
2 sin
2 sin 2 sin 2 sin
+ = = = =
=
++ =
=
x
C g y
z
i u i u
f f v g k j v g k j v g k
k w k w
v w i
u ju k g k
v
v i u j g k ug
u
v v
w
=
,
0
2
w u v
w
u g
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Coriolis force
( ) ( )
( )
2 sin
2 2 sinC C
H
H
v v
f v f fu u
fv i fu j f k v
= = = =
= =
H
uv
v=
2 sinf
Hv
Hk v
Hk v
k
c a b=
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Navier-Stokes Equation
( ) ( )1
2 Fm
dv vv v f p g k v f
dt t
= + = = +
dvdt
vt
( )v v
( )v v
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Navier-Stokes Equation
( ) ( )1
2 Fm
dv vv v f p g k v f
dt t
= + = = +
( )
= + + + = + +
= + + + = +
= + + + = +
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Navier-Stokes Equation
( )m m vt
=
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Scale analysis
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Scale analysis
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Geostrophic approximation
0i
i
f f= =
( ) ( )1 1
0
2( ) ( ) 0
C pH H
m H m H
f f
p v p f k v
+ =
= =
( )
( )
C HH
p HH
f v
f v
( )1
gs H
m
v k p
f
=
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Geostrophic approximation
( )
1
gs Hm
v k pf
=
0C p Zf f f+ + =
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Cyclostrophic wind
( ) ( )2
0
10
+ =
+ =
p ZH H
m
f f
p v
n r
A t hi i d
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Ageostrophic wind
t hi i d
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ageostrophic wind
ageostrophic wind
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ageostrophic wind
Vertical motion
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Vertical motion
( ) ( ) 0
10
g pV V
m
m
f f
pg
zp
gz
+ =
=
=
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