Applied Mathematics and Mechanics (English Edition, Vol. 20, No. 4, Apr. 1999)

Published by SU, Shanghai, China

A DISCUSSION OF NON-LINEAR MECHANISM ON SUBTROPICAL ANTICYCLONE' S EXTENDING/SttRINKING OVER EAST-ASIA IN SUMMER* Zhang Ren

Shi I-hnshen

Sha Wenyu

Air Force Institute of Meteorology, Nanjing 211101, P R China (Communicated by Lin Jianzhong; Received July 22, 1996; Revised May 22, 1997) Abstract:

Based on the actual circulation structure as well as weather characters over East-Asia subtropical region in summer, by using three-dimension non-linear forced/dissipated dynamic model, the activities of subtropical anticyclone over EastAsia have been studied and discussed. The potential enstrophy criteria of system stability have been derived and also been analysed. The criterion can provide useful reference for analysing and predicting subtropical anticyclone' s emending/shrinking as well as corresponding weather over East-Asia in sunroof.

Key words:

subtropicalanticyclone; potential emtrophy; stability criterion

Introduction The subtropical anticyclone ( subtropical high) over East-Asia region is an important synoptic system influencing this region's weather. The variations of this system's strength/position often decide whether the precipitation and temperature of East-Asia area is high or low. Some serious droughts and floods of Yangtze/Huaihe fiver area in history were mainly brought about by abnormal activity of subtropical anticyclone over East-Asia. East-Asia subtropical anticyclone has been studied for a long time, but the research concerning concrete prediction criterion about subtropical anticyclone' s middle/short period shift was rare. Recently, s o m e researches [1-3] show that the activity of East-Asia subtropical anticyclone was constrained by such factors as the difference between circulation structures/ patterns over East-Asia area and the weather system around this area. The study mentioned above stressed the importance of heating-forced factor caused by monsoon rain belt (meiyu band) over East-Asia continent and monsoon trough rain belt from west-pacific to south China sea as well as the strong cumulus convection nearby philippine, which influence and constrain the East-Asia subtropical anticyclone' s extending/shrinking to a great extent. We have also studied above questiom from viewpoint of perturbation energy production/dissipation, some results were obtained[4] . In this paper, we will Taa'ther study and exploration will be done on the system stability problems about East-Asia subtropical anticyclone' s developing/decaying and extending/ withdrawing from viewpoint of vortex, and induction will be made on perturbation potential entrophy criterion for predicting and estimating East-Asia subtropical anticyclone s variation.

* Project supported by an Air Force Basic Theory 441

Zhang Ren, Shi Hanshen and Sha Wenyu

442 1

Dynamical Model and Mathematical Treatment

1.1

M o d e l equations 25 ~ N was appointed center latitude, the monsoon trough rain belt over South China SeaWest Pacific (south rain belt) and monsoon rain belt over East-Asia continent (north rain belt ) were respectively appointed southern and northern boundaries, 500 hPa was assigned model study layer in vertical direction, this special East-Asia subtropical zonal region was assigned model research area. Resembling the treatment of document[4] , a three-dimension non-linear dynamic model (which was dispersed into two layers in vertical direction) including heat-forcing effect[5] and horizental vortex-dissipation effect was introduced:

2A----p+

fit + ~1 ~

~2~1 +

~+~3~

7 ~3+ B- oy2/Ox +J(03'v2o3) = 2-~ +Kh74~3'

o~

fl -- "~-2 I-fiX" x + J(~bl, ~ 2 ~ 1 ) -- -

1

1J(r

_aa (

+ ~3,~1 - ~3) =

1

2ApC,,p(q~l -

~3)

(1)

(2)

3

- 2Ap fo ka, -- AT]**)2o~2,

where ~b is perturtation flow function, ul = ~ l ( y ) , g 3 277 )2(Y), A -

Kh ~ 4 ~ 1 ,

(3)

= g3(Y), (a, - At/" )2 = (a, -

is a non-dimensional heat parameter, Kh is a

horizontal vortex dissipative coefficient, Ap = 200 hPa is a vertical difference strike, as is a static stability parameter, q~ is average saturation specific humidity, the footnotes 1, 2, 3 are respectively 700,500,300 hPa layers, the other symbols are common in meteorology. Boundary conditions: f'zxed boundary condition with southem rain belt boundary and northern rain belt boundary are used in y-direction; periodic boundary condition are used in x-direction. 1.2 Balance equation of p e r t u r b a t i o n potential e n s t r o p h y Based on the model equations, we introduced a potential enstrophy for reflecting the rotation of vortex system, the equilibrium equation of potential enstrophy cart be expressed as follows: dM dt - - KhDM + PM, (4) where

1 M = -~--<1 7 2 ~1 12 +1 7 2 ~3 [ 2 + l_(. f o~)p ] 2o'(y-) [ 7 ( ~ 1 - ~b3) [2>,

M is called general perturbation potential enstrophy. The first and the second term of M are general perturbation enstrophy of 700 hPa and 300 hPa level respectively in model area (L~ 9 [ - L, L ] ), which reflect the rotation intensity of vortex synoptic system in appointed levels. Because the East-Asia subtropical laigh belongs to dynamic high, corresponding to the subtropical anticyclone system at 500 hPa level over East-Asia region, it should be the anticyclone system (East-Asia subtropical high) with negative vorticity ( ~1 = 7 2 ~b 1<0) at 700 hPa level and cyclone system (the west-extending part of T u T r ) with positive v0rticity ( ~3 = 7 2 ~b3 > 0 ) at 300 hPa level, the more the absolute value of vorticity ( I ~ I, I ~3 I ) is, the greater the corresponding potential enstrophy ( I 7 2 ~1 12 , I 7 2 ~b3 12 ) is, and also the stronger the

Non-Linear Mechanism on Subtropical Anticyclone

443

subtropical anticyclone at 500 hPa level is. The third term of M indicates the vortex kinetic energy between 700 hPa and 300 hPa level, which also reflects the intensity of vortex movement in this assigned region, and in fact, it represents the intensity of subtropical vortex system at 500 hPa level. Where DM = ( I 7 3 ~bl Iz + I 7 3 ~b3 Iz ) is dissipation term of general perturbation potential enstrophy, which is mainly resulted from vortex diffusion. e.

_

2

--'~-y2 j--'~X. 7/ r

+ <(~ -- Oy2 / OX

(U3 -a~bl ~ -- ~1 a~b3/ a x ] 72(~bl - ~b3)) ~b3,~1 -- ~ b 3 ) V 2 ( r

72r

(fol

-- --4t'-~p] ( a ( y ) x

i/So/2 -~--~pl (a(y).J(~bl +

-- ~3)>

is called producing term of general perturbation potential enstrophy.

Where ( . ) = f i n [ . ]dxdy,g'2 = L, x [ - L,L] ,L, is wave length in direction of x , L is fixed boundary radius in direction of y, a ( y ) = 1/(a, - ;trl* )2(Y) is a meridional thermal distributed function at 500 hPa level. We know from equilibrium Eq. (4) that if the producing term is larger than the dissipating term of potential enstrophy (PM > Kh DM), then dM/dt > 0 general perturbation potential enstrophy will increase with time and the whole rotation of system will strengthen, corresponding to the special environment of East-Asia in summer, which indicates that East-Asia subtropical anticyclone system will stably develop and maintain. On the contrary, dM/dt < 0 indicates EastAsia subtropical anticyclone decaying and retreating from East-Asia continent. By analysing and researching the increase/decrease conditions of M as well as relevant physical mechanism and synoptic characters, finding out the criterion of system stability, we can analyse and predict the activity of subtropical anticyclone and corresponding weather over East-Asia area. By integrating along meridional direction, the thermal effect of both the southern and northern rain belts are coupled. Appointing wave solution, the stability problem can be translated into the problems of complex function eigenvalue and differential inequality. . . . . . l(fol 2 Assign PM = PM + PM ,PM = - ~ - ~ p ] (a(y)J(~bi + ~b3,~bl - ~b3) 72(~bl - ~b3)), the estimation formula as follows: 1) If al = a2 = a3, it means there are no thermal difference along meridional direction, then PM

~ O;

2) When there exists meridional thermal difference, then l(fo/2 [ PM** [ <~ "-ff -~p] max( I ty{ 1 - o'21 [ , [ (y~l _ o.~1 [ ) " ( [ J( r

+ ~b3, ~bl - ~b3 ) [ x

[ V2(~bl -- ~b3) [ ) .

The producing terms of potential enstrophy P;r and P~* will be treated respectively. Considering some subsidiary eigenvalue problem fn'st; then a difference inequality will be induced by introducing a embecling formula; next , by making a serial of careful estimation with variational method, the systematic potential enstrophy criterion of non-linear stability and the decaying estimation of general perturbation potential enstrophy are finally given out.

Zhang Ren, Shi Hanshen and Sha Wenyu

444

1.3

Subsidlnry eigenvalue problems a) Kh*,M max(P~/DM). Considering eigenvalue problem: 1/i.t = P~/DM~ variational problem: :

~(D,~ -

e 2 ; , ) = o,

(5)

where 8 is variational symbol. Assign G~ = a(y)(~s - ~ ) , then the Euler-Lagrange equation revelant to variational problem (5) can be given

276~bl + /z{-

Ul4) a~l -- 2g~3) 02~1

ax

axay

4

~pp

-

Go Oxx 72~b3 +

a~ + 2r a~ay/ :~31 }= o,

(6a)

~

2 7 6~3 + ~ {- ~4) a~3 8x

ar

g -~x +

-

2~3) a2~3 OxOy

+

1(:o/2( a ApI k G~ ~ 72~bl +

2c; a:rx a y / / } = o.

(6b)

Appoint wave solution: ~bl : 9z(y)exp{ik(x- ct)},~b3 = 93(y)exp{ik(x- ct)}, and inserting them into (6a) and (6b) equations, we can get what follows: 9~6) - 3kZg~4) -- k691 4- k4{39; - -~z/.tgl" --3-(a)u, 9, - i/zu~3) k-3 91 } -

ltSo/2 S ~pp/

ik/t[G'(9; - k293) + 6e~93 + 2G;9;] = O,

(7a)

966) - 3k293(*) - k693 + k*{39; - "-ffi,uk-13 ~.64)93 - i,u~63) k-3 93'}+ ik/z[G-(9] - k291) + < 9 , + 2G;913 : 0.

-ff ~

(7b)

Now, two different methods are used to estimate eigenvalue 1//z. Method 1 Make a change ex fi/~g~2) 1~ fi/zg~2) L~. 9, : P l - g g - l ~ ' ' 9~ : r 1 ~'~' and put them into (7a) and (7b) formulas, and then make following operations:

f2z (7a). ~ [ .expl--gj'- i/,t.] 1. + f-L L (7b). ~b; .expl--g J'- i/zg; ~ icty ~ } dy we can induce

-eLf ~ ~?~: I~l 12 + - ~-~,(I],j+3kZI2,j+3k4W~14+k612,.i)+12kZJ_L[( j.~l,3

(~3))2 I ~b3 12]dy +/~I(9~,93,G,) = 0,

(8)

where I(~,93,Cr

= -

•8 ~ t f~ , p ll~kffJ -~L [ ( c,9~)'9;

(c,9,)'9;

-

k 2 ~39~"

-

+ k2 9, 9 ; ] as.

(9)

By calculating,

1(91,93, Ga)

=

1[ fo/2,.rf ~ cz, ,,,(939{")dy ~-~p] ,~Lj_L

-

:f~J,(9~9;)ar].

(10)

Non-Linear Mechanism on Subtropical Anticyclone Using equal-parameter

445

i n e q u a l i t y [6'7] 9

2 ~ I~,i >>.;t~I~,i, /~,i >>. )t~I,,i,

i2,j

2 2 >~ A3I~,i,

j = 1,3,

(11)

where

;,

I2~.1 =

~

~2 ~

-

dy, W2~,1 =

-L dy'

4L 2'

rr

L~ ~ =

-

'

; I

-L dy i (2.36514

~--L--/

dy, i

=

0,1,2,3; j = 1,3

'

"

An estimate-equation can be got:

1 = tI12k2I(~~

+ [144k412(~~176

,u

+ 48k2]~-]'(~'i + 3k212'1 + ./=~.3

3k4W21,j + k612j) {fL (Ul")2 I q~l iz + (u3")2 I q~3 IZ}dy] 1/2

}/

~4~ ~ (/],~ + 3~/~.; + 3~'w,~, + r j= 1,3

1

F where

~(k) + ~/~2(k) + r](k) ~=Kh~,M,I,

=

k I G~ Im~ 32(22

(12)

+ 3 k 2 ) 1/'2 "

f o / 2 k3/ 16(2~A] + 3k222 + 3k4~2 ~-~p/

(3k422 + k6

+

k6) 1/2 +

),

r~(k) = max[max I ~, 12,max I ~3 12]/12k2( 22A2 + 3k222 + 3k4,~ + k6) 9 Method 2

Make operation

;-L" (7a)~o~" ( y ) d y + ?-L (7b)q~; (y)dy,

we cart induce

-- ~-~j(I2j + 3k 212.j + 3k 4121.j + k 6120,j) + k/A -L /ffil,3

u3I~(~3~3

)]dy

+ FI(~I,~3,G~)

= 0,

and further an equation and an inequality are given: k

1

m

t

_L[1/,l/m(~l~01 ) + U3Im(~O;~O; fL

)]dy +

1(~01,~o3, G )

F j= 1,3

24:(k) +

k'max(I Ul ]

~

, I ~3 Im~)'(Io 111.t + 10,311,3) '

~-]~(I~,i + 3k2122,i + 3k4I~,1 + k6I~,i)

~<

j= 1,3

2~(k)

+ 2(~

+ 3 k 4 ) V 2 ( k 6 + 3 k 2 ~ ) v2 = 2 ~ ( k )

+

O(k).

Finally the estimate-formula is shown

__1 /1 ~ 2~(k) + O(k) ~gh:M, 2 Combining (12) and (13), we have Kh,~r * ]9 " ~< min[K~M,1 , gh.M.2

(13) (14)

446

Zhang Ren, Shi Hanshen and Sha Wenyu

b) ,~M

--

wbere~=

II/93 ( ~

-

max(~/DM). (I V ( ~

~3) II 2L 2

~

+ ~3) 12 +1 V ( ~

- ~3) 12) + IID3(~a + ~3)112

II 9 II L is mode of L 2 ) 3y3

3xay2

Consider eigenvalue problem: 1 8" /t - DM =* ~(DM - / ~

9

= 0,

(15)

is variational symbol, the Euler-Lagrange equation relevant to (15) is 36 a6 V 6 ( ~ I + ~3) -- 2/z V 2 ( ~ l + ~3) + ~_ _6 ( ~ b 1 "1" ~3) + 0 x 4 0 y 2 ( ~ l + ~3) + 86 1 ax2ayg(r + tb3) + ay 6~(~b~ + tb3)] = 0.

(16)

By using the similar estimating method, we can estimate max(2 + k4,2k 2) J.u ~<2+ min(3k 4

+

A32,k 6

(17)

3k2232) "

+

c) 2nr = max(M/DM). 1 M Consider eigenvalue problem: /z - DM ~ ~(OM - :~M) = O, the corresponding Euler-Lagrange equation is 1( fo V 6 ~ + ~ { v 4 ~ -4-~--~p/ y) v ,( ~ ~b3) +a'(y) __a( 3y ~b, _

(18)

~b3)]}= 0 , (19a)

,

_

a

=0.

(19b) From (19a) to (19b), we can get -

+

1 fo ~pp/ • -

}-

o

Through the operation similar to (13), we get inequality 1 l a ( y ) Ira= " (124 + 124) ~u ~

22

+

k2 + i2,:

+

3k212,j

+

3k412,.i + k612d

1 l a(y) I~ /~ + k2 + (232 + 3kg)l/.Z(3k2A32 + k6)X~ .

Embeding inequality and the estimation of P;~* Theorem[6'7](Joseph,1973) Assumef(x, y) is a smooth function, a n d f I'r__• 2~/k is its period in direction of x , then the following formula is obtained:

(20)

1.4

= 0,

rL r2,ck 1 [~ 2kL } <:'> -- J_LJo f4dxdy ~< 2[~--A" ~ + 1.,<1 7 f 12>, (21) whereA = 1/(4k2L 2 + ~ ) , embeding this into inequality (21), an estimate-inequality can be

Non-Linear Mechanism on Subtropical Anticyclone

447

got:

I PM

I <~

--

--max

0-3-o'2 ) [ 2 k L + 1 } '/2 M1/2 0-3 L~7, in 9 ~'.

(22)

Stability criterion of potentlnl enstrophy and corresponding w e a k e n estimate Combine 1.3 and 1.4, the potential enstmphy can be regarded as Liapunov function, when following inequalities am true: 1.5

dttg*

Kh > min(K~.M.1,Kh.M.2) =

~a2 "max

0-3

'

(23a)

h.M,

0-'--'~ <" ~

[rtA ]''z + 1

•

gh - Kh',M 9 Ap (23b) M'(0) 1/2 fo ' where Kh',M.I, Kh'.*t,2, 2M are given by (12), (13) and (17) formulas respectively, M(0) is initial perturbatio n potential enstrophy of unit mass. Then, the foflowing differential inequality is obtained dt

~<

- (Kh-

2kL

K ~ M ) M + ~ ( f ~ A--p] ~-2a2max~ 1 [ ~

~i/2 + 1]

O"1

0"3

3 II. ;MM'a~/AM,

(24a) (24b)

M I t=o = M ( 0 ) .

From (24a) and (24b), we can solve a weakening estimation of perturbation potential enstmphy: M(t) M(O) [Kh - K~.M - F ( k ) M l / 2 ( t ) ] 2 <~ [Kh - K~.M - F(k)M1/2(O)]2 x

exp where F ( k ) --

{

Kh-Kh~'M t}, 2M ~-2a2max I

(25)

0-1

'

0-3

t~-~ 1'2 + 1

AM-

(23a) and (23b) are called potential enstrophy criterion of vortex weather system, when the criterion exist, the vortex synoptic system will weaken with time, and the decay conditions are described by formula (25). 2

Analysis and Discussion

From formulas (23), (12), (13) and (17), we know the factors which restrain and influence potential enstrophy criterion of vortex system stability am u l , u3, ( ~3 - ~1 ) ,0-1 ,a2, 0-3, k and L. Where ~ = 33 ~1/3 y3, u'3 = a3 ~3/3Y 3 and ( ~3 - ~1 ) they express the influence of zonal basic flow's N-S shear and vertical shear at high layer (300 hPa) as well as at low layer (700 hPa) over East-Asia subtropical region near 25~ on the East-Asia subtropical vortex system stability at 500 hPa layer.

Zhang Ren, Shi Hanshen and Sha Wenyu

448 1

1

1

al = (0", - tl7]* )2(Yl)' a2 = (a, - RT]* )2(Y2)' 0.3 = (as - ~r]* )2(Y3)' reflect the influence of thermal state and stratification stability at monsoon trough rain strip from South China Sea to West-Pacific ( y] ), at East-Asia subtropical area near 25~ ( Y2 ), and at EastAsia continent monsoon rain band ( Y3 ) , on the stability of East-Asia subtropical vortex system at 500 hPa layer respectively. k = 2rJLz indicate the stability state of synoptic system which has different zonal wavelength over East-Asia subtropical region. L express the possible influence of the distance between the southern rain belt and northern rain belt, on the East-Asia subtropical system's stability. ff the compound effect of above factors satisfy potential enstrophy criterion (23a), (23b), then the synoptic system is stable, whose perturbation potential enstrophy M will decay with time, vortex system will weaken and withdraw, otherwise, the weather system is unstable, whose M will increase with time, the vortex synoptic system will strength and develop. By analysing and calculating the physical mechanism and synoptic pattern based on formula (23), we can obtain following results: 1) In model area, as to the micro-weather system (k -,- oo ), whose potential enstrophy criterion indicates that the vortex system is stable, the general perturbation potential M decreases in the form of exponent with time, which means the small scale short-wave weather system is difficult to develop or maintain over East-Asia subtropical area. As to ultra-long wave weather system ( k -~ 0), if the initial potential enstrophy M (0) is sufficiently small, or the meridional thermal difference is little, the ultra-long wave system is still stable, whose potential enstrophy will decrease in the form of exponent with time, and this sort of planet-scale vortex synoptic system is also difficult to develop or maintain. 2) Calculated results show that, at 500 hPa layer of model area, the most unstable vortex system's scale ranges from 300 0 to 500 0 km, which means, when the system is unstable, the general perturbation potential enstrophy within this scale range increases most quickly, the vortex system is easy to develop quickly or the original vortex system intends to strengthen and maintain stable, when system is stable, the weather system within this scale ranges weakens most slowly and it indicates that the original vortex synoptic system decays slowly and maintains for some periods (as shown in Fig. 1 and Fig. 2 between 300 0 ~ 500 0 km wave domain). In summer periods of East-Asia subtropical area, the persistent cyclone system within above scale ranges is rare, but anticyclone system, say, the west pacific subtropical high 'zonal scale belongs to this "most unstable" ranges and maintains persistent. So, when system is unstable, they often extend toward the west/north and form a sort of strong and stable East-Asia subtropical anticyclone, while when system is stable, they don' t die at once, but weaken generally and withdraw toward the east. From above discussion, the EastAsia subtropical anticyclone' s strong/weak or advance/withdraw can be estimated or predicted by system stability's potential enstrophy criterion. 3) When East-Asia continent monsoon rain belt' or South China Sea-West Pacific monsoon trough' rainfall is heavy and its thermal force is outstanding, but centered at 25~ there are no precipication or the thermal effects between northern and southern rain belts are weak, and when the thermal difference between either of the two rain belts and 25~ is striking. At 500 hPa layer,

Non-Linear Mechanism on Subtropical Anticyclone

449

the system between the two rain belts will tend to be unstable, the corresponding vortex synoptic system's general perturbation potential enstrophy will increase with time, especially the East-Asia subtropical anticyclone' s developing is remarkable (as shown in solid lines of Fig. 1 and Fig. 2). Which express that the subtropical high maintain stably over the East-Asia, whose relevant weather is clear, hot, and persistent drought. In other words, persistent strong convective precipitation and marked meridional thermal difference are important factors which induce East-Asia subtropical vortex system to develop and strengthen, and benefit the East-Asia subtropical anticyclone to be stable and strong. On the contrary, as shown in dotted lines of Fig. 1 and Fig. 2. I

m

i

t

~-. 7 1.0

I .( x 10-z)

Khl L3

•

~0.5

6

\ l

;f

l

2

3

4

5

6

7

g

9

10

/~( x 10~)/km

t~( x *03)/kin Fig. 2

The first criterion' s calculation results of potential enstrophy, unstability domain is above t h e criterion K h / L 3 , s t a b i l i t y domain is below the criterion K h / L 3

Fig. 1

T h e second criterion' s initial potential enstrophy Mc (0) calculation results, unstability domain is above the criterion M , ( 0 ) , stability domain is below the criterion Me (0)

s/(*)N t

~,tllll 25

/ //

E

wind

i-s

Fig. 3

-4

o

4

ui ( y)/m/s

i'll

West

wind

The average patterns of zonal basic flow at 700 ~ layer in East.Asia subtropical region during stua,iier

East

wind Fig. 4

- 10 0 10 F~3(y)/m/s

20

30

West wind

T h e average patterns of zonal basic flow at 300 hPa layer in East-Asia subtropical region during summer

4) In East-Asia subtropical area, when southern monsoon in low layer is active, there will be monsoon low pressure forming or developing on the northern side, Tibetan high strengthen and extending toward the east, ~x)pical easterlies are strong in high layer, in this time, the meridional shear of zonal basic flow increase in both high and low layers, and vertical shear between high

450

Zhang Ren, Shi Hanshen and Sha Wenyu

layer (tropical easterlies) and low layer (southwest monsoon) becomes the largest. In this circulation structure and pattern (as shown in dotted lines of Fig. 3 and Fig. 4 ) , East-Asia subtropical vortex system tends to develop unstably, and it also induces West Pacific high to extend toward the East-Asia continent and benefit the East-Asia subtropical anticyclone to strengtben or maintain. When subtropical high systems both high layer (Tibetan high) and low layer (west pacific subtropical high) draws close further and tend to be overlapping, there are easterlies both high and low layer (as shown in solid lines of Fig. 3 and Fig. 4 ) , or when west pacific subtropical high and Tibetan high withdraw toward the east and the west respectively. In East-Asia subtropical model area, the system will tend to be stable, whose general perturbation potential enstrophy will weaken. It is the best circulation structure and pattern that induces West Pacific subtropical high withdrawing from East-Asia continent and makes East-Asia subtropical anticyclone system be difficult to maintain but decay or die. 5) Under the same conditions, when the distance between sourthem and northern rain belts is longer, then the l%~r synoptic system between the two rain belts at 500 hPa layer tends to be unstable, the synoptic scale vortex system is easy to develop and maintain, in this case, west pacific subtropical high extends toward the west and arrives in East-Asia continent, and becomes a strong and stable East-Asia subtropical anticyclone. On the contrary, the East-Asia subtropical system tends to be stable, the East-Asia subtropical anticyclone is difficult to develop or maintain. The theory analysis and discussion based on potential enstrophy criterion conform to the weather facts and diagnostic analysis, and the used model can generally express the circulation structure and the synoptic characters of real East-Asia subtropical region in summer, so the dynamic analysis and diagnostic calculation based on the potential enstrophy criterion can provide some theoretical reference for analysing and predicting East-Asia subtropical anticyclone 'shift/ strength as well as corresponding weather. References [ 1]

Yu Shihua, Wang Shaolong.A circulation mechanism about west pacific subtropical high's middle-period shift[J]. Marine Journal, 1989,11(3) :372 ~ 377 (in Chinese) [2] Yu Shihua, Yang Weiwu. Characters of subtropical monsoon circulation and its role in East-Asia summer circulation[ J ]. Applied Meteorology Journal, 1991,2(3) : 242 ~ 247 ( in Chinese) [ 3 ] Huang Ronghui, Li Weijing. Thermal source abnormality over tropical west pacific and its influence on East-Asia subtropical high as well as the physical mechanism in summer[ J]. Science of Atmosphere, 1989,107 ~ 116 (in Chinese) F4] Zhang Ren, Shi I-Ianshen. A study of non-linear stability on the west pacific subtropical high[ J ]. Science of Atmosphere, 1995,19(6) :687 ~ 700 (in Chinese ) [5] Jule G Chamey, Amt Eliassen. On the growth of the hurricane depression[ J]. J Atmo Sci, 1964,21(1) :68 ~ 75 [6] Adelina Georgescu. Hydrodynamic Stability Theory [ M ]. London: Martinus Nijhoff Publishers, 1985 Daniel D loseph. Stability of Fluid Motions, I [M] .New York: Springer-Verlag, 1976