Observations Summary: Review ■Zonal-mean flow: Ferrel Cell:an indirect cell centered at 40-60 degree,with strong seasonal variation in N.H. Westerly jet:surface westerlies centered at 40-60 degree ■ Eddies:transient eddies are dominant with stationary eddies only obvious in N.H. ■Kinetic energy ■Momentum flux ■Heat flux 授课教师：张洋3
3 Observations \ 授课教师：张洋 n Summary: n Zonal-mean flow: n Ferrel Cell: an indirect cell centered at 40-60 degree, with strong seasonal variation in N.H. n Westerly jet: surface westerlies centered at 40-60 degree n Eddies: transient eddies are dominant with stationary eddies only obvious in N.H. n Kinetic energy n Momentum flux n Heat flux Review
The Ferrel Cell eddy-zonal flow interaction(T)Review The simplified equations: Momentum equation: u= Ot ∂([u*wD+fu+[F] 8y Continuity equation: y+=0 ay *Op Thermodynamic equation: ∂) 00s +0加 ∂(0v* (台 2 R/Cp Q] 8t 8y Cp ()-(,+(品)+()+品 Under the quasi-geostrophic approximation (Ro<1) 授课教师：张洋4
@[v] @y + @[!] @p = 0 Under the quasi-geostrophic approximation (Ro ⌧ 1) @[u] @t = @([u⇤v⇤]) @y + f[v]+[Fx] @[✓] @t + [!] @✓s @p = @([✓⇤v⇤]) @y + ✓po p ◆R/cp [Q] cp 授课教师：张洋 4 The Ferrel Cell eddy-zonal flow interaction (I) ✓ d dt◆ p = ✓ @ @t ◆ p + u ✓ @ @x ◆ p + v ✓ @ @y ◆ p + ! @ @p n Momentum equation: n Continuity equation: n Thermodynamic equation: n The simplified equations: Review
The Ferrel Cell The balance equations: Review Tropopause fu Ofu*v*] ∠0 8y Ferrel Cell: eddy-driven, 70t auoD+f网+F到 by indirect cell a0。_a0*w ∠0 00s Oy wOp a01>0 by 00s a(0*u*]) R/CP IO + Po ∂t ap by Cp Boundary fv ~rusurf>0 layer Ground Subtropics Latitude Subpolar 5
! @✓s @p ⇠ @[✓⇤v⇤] @y < 0 ! @✓s @p ⇠ @[✓⇤v⇤] @y > 0 fv ⇠ @[u⇤v⇤] @y < 0 5 n The balance equations: The Ferrel Cell @[✓] @t + [!] @✓s @p = @([✓⇤v⇤]) @y + ✓po p ◆R/cp [Q] cp @[u] @t = @([u⇤v⇤]) @y + f[v]+[Fx] Ferrel Cell: eddy-driven, indirect cell Review
及图乐 Outline Observations The Ferrel Cell ■ Baroclinic eddies Review:baroclinic instability and baroclinic eddy life cycle Eddy-mean flow interaction,E-P flux ■ Transformed Eulerian Mean equations Eddy-driven jet Energy cycle 授课教师：张洋6
授课教师：张洋 6 Outline n Observations n The Ferrel Cell n Baroclinic eddies n Review: baroclinic instability and baroclinic eddy life cycle n Eddy-mean flow interaction, E-P flux n Transformed Eulerian Mean equations n Eddy-driven jet n Energy cycle
Baroclinic eddies ■Instability: -baroclinic instability-Review Phenomenon:Given a basic flow with perturbations at the initial moment,if the perturbation grows with time,the basic flow is always taken unstable. Mathematics:P&Aet,a>0 (相对于波动解：P Aeiwt) ■Energy': 能量源→ 扰动动能！ Linear Instability:the instability that arises in a linear system. 授课教师：张洋7
授课教师：张洋 7 Baroclinic eddies - baroclinic instability n Instability: n Phenomenon: Given a basic flow with perturbations at the initial moment, if the perturbation grows with time, the basic flow is always taken unstable. n Linear Instability: the instability that arises in a linear system. n Mathematics: P _ Ae↵t , 9 ↵ > 0 P _ Aei!t (相对于波动解: ) n Energy: 能量源 扰动动能 Review