第四章 : 中纬度的经向环流系统 (II) - Ferrel cell, baroclinic eddies and the westerly jet 授课教师 : 张洋

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1 第四章 : 中纬度的经向环流系统 (II) - Ferrel cell, barocliic eddies ad the westerly jet

2 Observatios - Eddy fields Review Strog barocliic eddy activity L R O(1000km) Syotic time scale (2-8 days) \ [AB] = [(Ā + A0 )( B + B 0 )] = [Ā B]+[A 0 B 0 ] = [([Ā]+Ā )([ B]+ B )] + [A 0 B 0 ] = [A] [B]+[Ā B ] + [A 0 B 0 ] A =[Ā]+Ā + A 0 2

3 Observatios Summary: Review Zoal-mea flow: Ferrel Cell: a idirect cell cetered at degree, with strog seasoal variatio i N.H. Westerly jet: surface westerlies cetered at degree \ Eddies: trasiet eddies are domiat with statioary eddies oly obvious i N.H. Kietic eergy Mometum flux Heat flux 3

4 The Ferrel Cell eddy-zoal flow iteractio (I) Start from the equatios: Mometum equatio: du dt Review + F x Cotiuity equatio: Thermodyamic equatio: r =0 d l dt = Q c T Decomose ito zoal mea ad eddy comoets: A @ = + u + v 4

5 The Ferrel Cell eddy-zoal flow iteractio (I) Start from the equatios: Review Cotiuity equatio: Thermodyamic =0 Uder the quasi-geostrohic aroximatio (R o 1), above equatios ca be simlified. v ]) ]) v = + @([! + f[v]+[f x ] R/c [Q] c 5

6 The Ferrel Cell eddy-zoal flow iteractio (I) Start from the Simlificatio: v ]) v ]) + f[v]+[f + R/c o [Q] c + =0 For midlatitude large scale flow, the eddy comoets of the meridioal heat ad mometum trasorts are domiat. (recall the [u ] [ ] ([ ][v]) From the o Horizotal variatio of the stratificatio is [u ([ ][!]) [!]@ 6

7 The Ferrel Cell eddy-zoal flow iteractio (I) Review The simlified equatios: Mometum equatio: v + =0 + f[v]+[f x ] Thermodyamic +[!]@ v ]) + R/c o [Q] @ = + u + v Uder the quasi-geostrohic aroximatio (R o 1) 7

8 The Ferrel Cell Review The balace equatios: v ] < s v ]) + f[v]+[f x ] < s v ] > +[!]@ v ]) + R/c o [Q] c 8

9 The Ferrel Cell Review The balace equatios: v ] < s v ]) + f[v]+[f x ] < s v ] > +[!]@ v ]) + R/c o [Q] c 9

10 The Ferrel Cell Review The balace equatios: v ] < 0 Ferrel Cell: eddy-drive, idirect s v ]) + f[v]+[f x ] < s v ] > +[!]@ v ]) + R/c o [Q] c 10

11 Outlie Observatios The Ferrel Cell Barocliic eddies Review: barocliic istability ad barocliic eddy life cycle Eddy-mea flow iteractio, E-P flux Trasformed Euleria Mea equatios Eddy-drive jet The eergy cycle 11

12 Observed Barocliic eddies Strog barocliic eddy activity i the midlatitudes Syotic time scale (2-8 days) L R O(1000km) 12

13 Observed Barocliic eddies Strog barocliic eddy activity i the midlatitudes Syotic time scale (2-8 days) L R O(1000km) 13

14 Observed Barocliic eddies 南北北能量量输送 大 气输送 Strog barocliic eddy activity i the midlatitudes Syotic time scale (2-8 days) L R O(1000km) Barocliic eddies: the domiat cotributio 14

15 Observed Barocliic eddies 15

16 Observed Barocliic eddies Mars 授课教师 张洋 16

17 Observed Barocliic eddies 斜压扰动是中纬度各种日常天气现象背后主要的物理过程 更 是维持大气环流和地球大气能量南北输送以及现在的地球气 候状态的最主要动力机制 此外斜压扰动也是海洋和其他一 些行星大气中的主要动力过程 授课教师 张洋 17

18 Outlie Observatios The Ferrel Cell Barocliic eddies Review: barocliic istability ad barocliic eddy life cycle Eddy-mea flow iteractio, E-P flux Trasformed Euleria Mea equatios Eddy-drive jet 18

19 Barocliic eddies - barocliic istability Istability: Pheomeo: Give a basic flow with erturbatios at the iitial momet, if the erturbatio grows with time, the basic flow is always take ustable. Mathematics: P _ Ae t, 9 >0 P _ Ae i!t ( 相对于波动解 : ) Eergy: 能量量源 扰动动能 Liear Istability: the istability that arises i a liear system. 19

20 Barocliic eddies - barocliic istability Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. 20

21 Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. 圆盘实验 I equilibrium z w Sashot from x co to z co z z warm cold x Above from Prof. Fag Jua s class slides cold warm x 21

22 Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. z co Sashot from to Satellite view at south ole, from NASA. 22

23 Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. z co Sashot from to Satellite view at south ole, from NASA. 23

24 Barocliic eddies - barocliic istability Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. 24

25 Barocliic eddies - barocliic istability Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. desity icreasig low desity high temerature B desity decreasig C warm )) A L cold high desity low temerature From A to B: egative buoyat If A ad C are iterchaged: PE gdz PE = g( A z A + C z C C z A A z C ) = g(z A z C )( A C ) = g z PE = + L )L Assume small ad PE = gl 1 25

26 Barocliic eddies - barocliic istability Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. desity icreasig From A to B: egative buoyat If A ad C are iterchaged: low desity high temerature desity decreasig warm )) B A L cold C high desity low temerature If < PE gdz PE = gl 1 is called mixig sloe., a loss of otetial eergy. If = 1 2, PE is strogest. 26

27 Barocliic eddies - barocliic istability Barocliic Istability - is a istability that arises i rotatig, stratified fluids that are subject to a horizotal temerature gradiet. Eergetics: PE KE low desity high temerature B desity icreasig Mathematics: desity decreasig )) A C high desity low temerature Liear Barocliic Istability Liear barocliic system Eady s model (1949) Charey s model (1947) 27

28 Barocliic eddies - liear barocliic istability Eady s model (1949) Charey s model (1947) Eady, E Tellus, 1,

29 Barocliic eddies - liear barocliic istability Eady s model Charey s model Eric Thomas Eady ( ) 29

30 Barocliic eddies - liear barocliic istability JULE CHARNEY was oe of the domiat figures i atmosheric sciece i the three decades followig World War II. Much of the chage i meteorology from a art to a sciece is due to his scietific visio ad his thorough commitmet to eole ad rograms i this field. -- by Norma Phillis Charey s model 30

31 Barocliic eddies - liear barocliic istability Eady s model (1949) Charey s model (1947) a) The basic zoal flow has uiform vertical shear, U o (Z) = Z, is a costat b) The fluid is uiformly stratified, N 2 is a costat. The most distiguished differece with Eady s model is that beta effect is cosidered. c) Two rigid lids at the to ad bottom, flat horizotal surface, that is! = 0 at Z = 0 ad H. d) The motio is o the f -lae, that is =0 31

32 Barocliic eddies - liear barocliic istability Liear barocliic system: Eady model Charey model Small amlitude assumtio 小扰动 Normal mode assumtio 标准波形 Obtai the solutios, e.g. istability coditios growth rate most ustable mode Variable = Basic state + Perturbatio u(x,t)=u(z)+u 0 (x,t) u 0 (x,t) U(z) Liearized PV q q 2 + q + f 2 o s y + f 2 @ 0 N N 标准波形法, 带 入 方程和边界条件 : 0 i(k x!t) (x,t)=ae Fid the coditios for o-trivial solutios ad Ci >0 32

33 Barocliic eddies - liear barocliic istability Coclusios: Necessary coditio for barocliic istability: PV gradiet chages sig i the iterior or boudaries (Charey-ster theory), accordig to which the midlatitude atmoshere is barocliic ustable. Differet models. i.e. Eady ad Charey models have more rigorous coditios. Growth rate: Most ustable mode: Discussio = kc i 0.3 f o N Normal mode assumtio k 1 max / L 1 d = Eady Small amlitude assumtio, liearizatio Assumtio: uiform vertical shear of the zoal flow i both Eady ad Charey models! NH f o 1 k 1 max / f o N Charey 33