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Assignments 3 Question#1:Hadley cell under different forcing Angular momentum: 1.15 日E(φ，) =1- 2 [u=2a in2Φ 1.1 三UM CoSΦ 1.05 Thermal wind relation: 1 fu(0）-wol+tanu2()-2o1= gH∂© u0.95 a日。0b 0.9 0.85 日E(中，) (0)-(φ) D2a2 sin Θ。 1-△a63-+A(疗-》 日o 2gH cos2 0.8 ---Held -New 0.75 Need to know 白(0) 0.2 0.4 0.6 0.8 sinφ 日. 授课教师：张洋 2⇥˜ (0) ⇥o 授课教师：张洋 2 Assignments 3 Question#1: Hadley cell under different forcing [u] = a sin2 cos ⌘ UM ˜ - vertically averaged potential temperature o - reference potential temperature f[u(H) u(0)] + tan a [u2(H) u2(0)] = gH ao ⇥˜ ⇥ 授教：洋 19 Held-Hou model -Thermal wind relation ! Thermal wind relation: = p fu + u2 tan a = 1 a ⇥ ⇥ From steady state momentum equation f[u(H) u(0)] + tan a [u2(H) u2(0)] = 1 a ⇥ ⇥ At z=H and Z=0 [(H) (0)] ⇥ z = g o Hydrostatic balance: ⇥(H) ⇥(0) H = g ˜ o Vertical integral from 0 to H ! Angular momentum: Thursday, September 30, 2010 [u] = a sin2 cos ⌘ UM ˜ - vertically averaged potential temperature o - reference potential temperature f[u(H) u(0)] + tan a [u2(H) u2(0)] = gH ao ⇥˜ ⇥ 授教：洋 19 Held-Hou model -Thermal wind relation ! Thermal wind relation: = p fu + u2 tan a = 1 a ⇥ ⇥ From steady state momentum equation f[u(H) u(0)] + tan a [u2(H) u2(0)] = 1 a ⇥ ⇥ At z=H and Z=0 [(H) (0)] ⇥ z = g o Hydrostatic balance: ⇥(H) ⇥(0) H = g ˜ o Vertical integral from 0 to H ! Angular momentum: Thursday, September 30, 2010 [u] = a sin2 cos ⌘ UM ˜ - vertically averaged potential temperature o - reference potential temperature f[u(H) u(0)] + tan a [u2(H) u2(0)] = gH ao ⇥˜ ⇥ 授教：洋 19 Held-Hou model -Thermal wind relation ! Thermal wind relation: = p fu + u2 tan a = 1 a ⇥ ⇥ From steady state momentum equation f[u(H) u(0)] + tan a [u2(H) u2(0)] = 1 a ⇥ ⇥ At z=H and Z=0 [(H) (0)] ⇥ z = g o Hydrostatic balance: ⇥(H) ⇥(0) H = g ˜ o Vertical integral from 0 to H ! Angular momentum: Thursday, September 30, 2010 [u] = a sin2 cos ⌘ UM f[u(H) u(0)] + tan a [u2(H) u2(0)] = gH ao ⇥˜ ⇥ Set u(0) = 0 2⇥ sin ⇥a sin2 cos + tan a ⇥2a2 sin4 cos2 = gH ao ⇥˜ ⇥ Integrate with respect to ˜ (0) ˜ () o = ⇥2a2 2gH sin4 cos2 授教：洋 20 Held-Hou model -Thermal wind relation ! Thermal wind relation: ! Angular momentum: Thursday, September 30, 2010 [u] = a sin2 cos ⌘ UM f[u(H) u(0)] + tan a [u2(H) u2(0)] = gH ao ⇥˜ ⇥ Set u(0) = 0 2⇥ sin ⇥a sin2 cos + tan a ⇥2a2 sin4 cos2 = gH ao ⇥˜ ⇥ Integrate with respect to ˜ (0) ˜ () o = ⇥2a2 2gH sin4 cos2 授教：洋 20 Held-Hou model -Thermal wind relation ! Thermal wind relation: ! Angular momentum: Thursday, September 30, 2010 Need to know 0 0.2 0.4 0.6 0.8 1 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 sin E/o Held New ⇥E(, z) ⇥o = 1 2 3 HP2(sin ) + v( z H 1 2 ) ⇥E(, z) ⇥o = 1 H(sin3 1 4 ) + v( z H 1 2 )