Chapter1-2

(11)
We obtain the following two equations:
2 F N 2F 0 2 z
(12)
U V P 0 x y 0 t
Let
(13)
1 , where H is the “equivalent depth”. gH
The solution of Eq. (12) is
Gill’s solution for (a, b) heating symmetric about the equator, (c,d) heating antisymmetric about the equator.
Exp. 1: heating forced in the first e is a barrier layer in Tropical Western Pacific
The seasonal variation of the precipitation and barrier layer depth (shadow)
Specific area Mignot et al., 2007
(13)’
U 1 P yV t 0 x V 1 P yU t 0 y
If we look for the solution in the form of
U(x, y,t) u(y) V (x, y,t) v(y) ei(kx t ) P(x, y,t) p(y)
p (1) x p (2) y
1 p (3) 0 g 0 z 0
u v w 0 (4) x y z
( 0 N 2 / g)w 0 (5) t
g N where is the Brunt-Vaisala frequency. 0 z
6. Equatorial Wave Dynamics in Ocean and Atmosphere
The governing equations, u 1 by making hydrostatic yv t 0 and Boussinesq approximations, are: v 1 yu t 0
w 和 a 分别为海面10米以上风速和空
气密度。
4. Wind driven Ocean Circulation
North
0
thermocline
Upwelling downwelling Eastwards Geostrophic current and Westerly Westwards Geostrophic current and Eeasterly Ekman current
Chapter 1: Background
1. Atmosphere circulation 2. Air-Sea interaction in Tropical synoptic system: Tropical Easterly wave,Tropical Cyclone; 3. Flux at air-sea boundary 4. Wind driven Ocean Circulation 5. Upper Mixed Layer in Ocean and its heat balance 6. Equatorial Wave Dynamics in Ocean and Atmosphere
4.Wind driven Ocean Circulation
Ocean circulation in upper layer Pacific
v curl ( )

5. Upper Mixed Layer in Ocean and its heat balance
Tendency Eq of the T
Thermocline anomaly
U>0, h<0 U<0, h>0
Velocity anomaly
The Gill (1980) Atmospheric Model
Forced Wave
200 mb
500 mb
Q
U(z)
1000 mb
Warm SST
Q T '
(2) Forcing Wave in tropical atmosphere
Mixed layer
Tm Qnet w (T T ) um Tm e m d t 0c p h h
Thermocline layer
Qn et Qh Qe Qs Q l
Which term is the most important in Temperature variation of upper mixed layer?
w 1 2 p z 0 N 2 z 2 t
(8)
Substituting Eq. (8) into Eq. (4) results in
u v 1 2 p x y 0 N 2 z 2 t
(9)
We assume that
u(x, y, z,t) U(x, y,t) v(x, y, z,t) F(z) V (x, y,t) p(x, y.z,t) P(x, y,t)
(10)
then Eq. (9) becomes
U(x, y,t) V (x, y,t) 1 2 F(z) x y N 2 z 2 1 P(x, y,t) F(z) 0 t
Qh
(0.44 + 0.063 U10) X 10-3
1.35 X 10-3 0.9 X 10-3 2.5 X 106 J/kg kg(water vapor)/kg (air) kg(water vapor)/kg (air) W/m2 W/m2 K or °C K or °C
感热通量
潜热通量 Qe aCL LE w (qs qa )
v(y) 2 n!
n
(15)


1/2
e
y 2 /2
H n (y)
(16) (17)

k
2 2
k

2n 1, n 0,1, 2,K
H n (y) is Hermite polynomials
The equation (17) is the dispersion relation of equatorially trapped waves.
F(z) A cos(mz) B sin(mz)
N N m N is called the vertical wave number. c gH
Equations (13), (1), and (2) becomes
U V 1 P gH 0 x y 0 t
Free Wave
12.6 year -1
Thermocline anomaly
U>0, h>0 U<0, h<0
Velocity anomaly
Horizontal Structure of Oceanic Rossby Wave (n=1)
Free Wave
12.6 year -1
(1)’
(2)’
(14)
we get the second order of the differential equation (non-dimensional):
2 v(y) 2 k k 2 y 2 v(y) 0 y 2
The solution of Eq. (15), with BC of v(y) 0 as y , is:
1/2
(5) / z and (3) / t result in:
w g z 0 N 2 z t g 1 p 0 t 0 z t
(6)
(7)
After combinating of Eqs. (6) and (7), we get that
2 k2
k

1
Dispersion Diagram of Equatorially Trapped Waves
Free Wave
Frequency
Wave number
Westward propagating Eastward propagating
Horizontal Structure of Oceanic Kelvin Wave
2 k2
(1). Inertial-gravity wave:
k

2n 1
(17)
For high frequency, Eq. (17) becomes
k 2 2n 1
k 2 k 2n 1
(2). Rossby wave:
For low frequnecy, Eq. (17) becomes (3). Rossby-gravity wave: For n=0, Eq. (17) becomes We have two roots:
复习

Flux at air-sea boundary
符号 Cp 空气的比热 变量 取值与单位 1030 J· -1 · -1 kg K
风应力
CD a w w
Qh aCpCs w (Ts Ta )
CD
CL CS LE qa qs Qh Qe Ta Ts
拖曳系数
潜热交换系数 感热交换系数 蒸发潜热 10米大气的比湿 海面大气的比湿 感热通量 潜热通量 10米的气温 SST
Day=3
Day=4