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1 NumRu::GPhys::EP Flux 7 2 9

2 NumRu::GPhys::EP Flux 2 2 NumRu::GPhys::EP Flux EP A /02/9

3 NumRu::GPhys::EP Flux 2 NumRu::GPhys::EP Flux Elissen-Plm EP., EP. Plumb Tky-Nkmur. NumRu::GPhys::EP Flux., NumRu::GPhys::EP Flux,, NumRu::Derivtive NumRu::GPhys::Derivtive /02/9

4 NumRu::GPhys::EP Flux 3 2 NumRu::GPhys::EP Flux NumRu::GPhys::EP Flux. Andrews et l ,., λ, φ. z z H lnp/p s, H R dt s g H, R d R, w R d R/w, T s, g 0, p, p s. p s. 2005/02/9

5 NumRu::GPhys::EP Flux EP s EP, EP,. EP u v ˆF φ σ cos φ θ u v, 2.2 ˆF z σ cos φ f cos φ u u φ w 2.2b. ˆF φ, ˆFz EP φ, z.,. u, v, w,, u, v, w cos φ dλ dt, dφ dt, dz dt. θ,. σ σ 0 z exp, 2.3 s H., 0. f 0 z s e z /H, s p s /RT s f 2Ω sin φ 4π T rot sin φ 2.4. Ω, T rot., T rot., Andrews et l. 987 EP u v F φ 0 cos φ θ u v 2.5 u cos φ Fz φ v 0 cos φ f θ u cos φ w. 2.5b F φ, F z EP φ, z. F y, F z ˆF y, ˆ F z. F y, F z s ˆF y, ˆ Fz /02/9

6 NumRu::GPhys::EP Flux , v, w. v v v 0 0 v σ v θ σ w w + cos φ φ b 2.4 EP, TEM u. u t + v u cos φ f + w u cos φ φ X σ cos φ ˆF , F. F cos φf φ + F z 2.9 cos φ φ 2.6 Ψ σv Ψ g 2π cos φ, σw Ψ g 2π 2 cos φ φ b 2005/02/9

7 NumRu::GPhys::EP Flux 6. Ψ, 2. z p Ψ p H p Ψ 2., p 0 Ψ 0 Ψ θ, p 2π cos φ g p 0 v dp EP Flux..,,. p z H log, 2.3 p 00 p p 00 exp z 2.3b H p, p 00. θ w, T, ω Dp/Dt w, θ. w, θ. w ωh/p 2.4 κ p00 θ T, κ R/C p 2.5 p R, C p. 2005/02/9

8 NumRu::GPhys::EP Flux 7 A EP... EP... Andrews et l du dt f + u tn φ v + Φ cos φ λ X, A. dv dt + f + u tn φ u + Φ φ Y, A.b Φ Rθe κz/h, A.c H u cos φ λ + v cos φ φ + 0 0w 0, A.d dθ dt Q, A.e 2005/02/9

9 NumRu::GPhys::EP Flux 8 Φ, X, Y λ φ, κ R d /c p c p. Q, Q J C p e κz /H. J. 2., A, φ, z, t Aφ, z, t 2π Aλ, φ, z, t dλ 2π 0 A.2. A A A A A.3., A 0, A/λ 0. A. t u + u + u + u cos φ λ u + u + v + v φ u + u + w + w u + u f + tn φ u + u v + v + cos φ λ Φ + Φ X + X, A.4 t v + v + u + u cos φ λ v + v + v + v φ v + v + w + w v + v + f + tn φ u + u u + u + φ Φ + Φ Y + Y, A.4b Φ + Φ Re κz/h θ + θ, A.4c H cos φ λ u + u + φ {v + v cos φ} + 0 0w + w 0, A.4d t θ + θ + u + u cos φ λ θ + θ + v + v φ θ + θ + w + w θ + θ Q + Q A.4e 2005/02/9

10 NumRu::GPhys::EP Flux 9.,, u t + v t + u u cos φ λ + v u φ + w u tn φ fv u v + Φ cos φ λ X u t u u cos φ λ u u cos φ λ u u cos φ λ v u φ v u φ v u φ w u u u w w + fv + tn φ uv + tn φ u v + tn φ u v cos φ Φ λ + X, u v cos φ λ + v v φ + w v tn φ + fu + u2 + Φ φ Y v t u v cos φ λ u v cos φ λ u v cos φ λ v v φ v v φ v v φ w v v v w w fu 2 tn φ uu tn φ u 2 cos φ Φ Re κz/h θ Φ H + Re κz/h θ, H u cos φ λ + v cos φ + φ 0 0w u cos φ λ + φ v cos φ 0 t + u cos φ λ + v φ + w Q t u cos φ λ u cos φ λ u cos φ Φ φ + Y, 0w, λ v φ v φ v φ w w w + Q A.5 A.5b A.5c A.5d A.5e 2005/02/9

11 NumRu::GPhys::EP Flux 0. A.5, u t + v u φ + w u tn φ fv u v X u u cos φ λ u u v w φ + tn φ u v, A.6 v t + v v φ + w v tn φ + fu + u2 + Φ φ Y v u cos φ λ v v v w φ tn φ u 2, A.6b Φ Re κz/h θ 0, H v cos φ cos φ φ + 0 0w 0, t + v φ + w Q u cos φ λ v w φ A.6c A.6d A.6e. A.5, A.6 u cos φ λ + φ v cos φ + 0 0w 0 A.7. A.7 A.6. A.7 u u u cos φ λ + v u φ tn φ u v + u w u w 0 A.8 A.6 u t + v u φ + w u tn φ fv uv X 2 u u cos φ λ u u v w φ v u φ + 2 tn φ 2 u u cos φ λ u 2 cos φ λ 0, u v φ v u φ + 2 tn φ u v cos 2 φ φ v u cos 2 φ, w u w u 0 0 u w 0 0w u u v u w 0 0 u w 2005/02/9

12 NumRu::GPhys::EP Flux, u t + v u φ + w u tn φ fv u v X cos 2 φ φ v u cos 2 φ 0 0w u. A.6, A.7 v u v cos φ λ + v v φ + tn φ v 2 + v w v w 0 A.9 A.6 v t + v v φ + w v tn φ + fu + u2 + Φ φ Y. v u cos φ λ v v v w φ tn φ u 2 u v cos φ λ v v φ + tn φ v 2 v w 0 0 v w v u cos φ λ u v cos φ λ u v 0, cos φ λ v v φ v v φ + tn φ v 2 cos φv cos φ φ 2 w v w v 0 0 v w 0 v 0 w A.0 v t + v v φ + w DP vz + fu + tn φ cos φv cos φ φ 2 u2 + Φ φ Y tn φ u v w. A.6, A.7 θ u θ cos φ λ + v θ φ tn φ θ v + θ w θ w 0 A. 2005/02/9

13 NumRu::GPhys::EP Flux 2 A.6 t + v φ + w Q.. u cos φ λ v w φ u θ cos φ λ v θ φ + tn φ θ v θ w 0 0 θ w u cos φ λ u θ cos φ λ u θ 0, cos φ λ v φ v θ φ + tn φ θ v cos φv θ cos φ φ w w θ 0 0 θ w 0 w 0 θ t + v φ + w Q cos φ φ cos φv θ 0 0 w θ,. 2005/02/9

14 NumRu::GPhys::EP Flux 3 u t + v u φ + w u tn φ fv cos 2 φ u v X φ v u cos 2 φ 0 v t + v v φ + w v tn φ + fu + cos φ φ v 2 cos φ 0 0w u, A.2 u2 + Φ φ Y tn φ 0v w u 2, A.2b Φ Re κz/h θ 0, H cos φ φ v cos φ + 0 0w 0, A.2c A.2d t + v φ + w Q cos φ φ v θ cos φ 0 0w θ. A.2e.3 A.2 EP,. EP,. v v v 0 0 A.3 w w + A.3b cos φ φ u v F φ 0 cos φ θ u v u cos φ Fz φ v 0 cos φ f θ u cos φ w 2005/02/9

15 NumRu::GPhys::EP Flux 4. A.2 A.3, A.3 { } v + v cos φ φ 0 0 cos φ { } w 0, cos φ φ cos φ φ v cos φ + 0 0w { } + v cos φ φ 0 0 cos φ 0 { } v cos φ φ 0 0 cos φ 0 { } v cos φ φ 0 0 cos φ 0 { } v cos φ 0 φ 0 cos φ 0 0.,. { 0 { 0 { } 0. cos φ φ } cos φ φ } 0 φ { } 0 φ cos φ φ v cos φ + 0 0w 0. A /02/9

16 NumRu::GPhys::EP Flux 5 u. A.2 A.3, A.3 u t + v + v u 0 0 φ + w u cos φ φ f v + v 0 0 tn φ u v + v 0 0 X u t + v u u + w φ u t + cos 2 φ φ v u cos 2 φ 0 0w u, fv tn φ u v X cos 2 φ φ v u cos 2 φ + u cos φ φ + f v w u v u 0 0 φ + tn φ u v 0 0, v cos φ φ 0 2 cos 2 φ φ 0v u cos 2 φ + u cos φ φ + f 0 cos φ 0 0 cos φ 0 cos φw u v u 0 0 φ + tn φ u v 0 0 A.5 u cos φ + w u fv X 2005/02/9

17 NumRu::GPhys::EP Flux cos 2 φ φ 0v u cos 2 φ cos 2 φ 0 cos φ u φ + f 0 cos φ 0 0 cos φ 0 cos φw u v u φ 0 v θ u 0 φ + tn φ v u 0 0 tn φ 0 v θ 0 u 0 2 cos 2 φ φ 0v u cos 2 φ + 0 cos φ u φ + 0 v θ u 0 tn φ φ 0 v θ u 0 + f 0 cos φ 0 0 cos φw u v u tn φ v u φ cos 2 φ φ 0v u cos 2 φ + 0 cos φ u φ cos 2 0 cos 2 φ v θ u φ 0 cos 2 φ tn φ v θ u φ + f 0 cos φ 0 0 cos φw u + cos φ v u 0 cos φ 0 + cos φ tn φ v u φ cos 2 φ φ 0v u cos 2 φ + 0 cos φ u φ cos 2 0 cos 2 φ v θ u + cos φ φ φ φ 0 cos φ v θ u + f 0 cos φ 0 0 cos φw u + 0 cos φ 0 u φ + sin φu v θ 0 A /02/9

18 NumRu::GPhys::EP Flux cos 2 φ φ 0v u cos 2 φ + 0 cos φ u φ cos 2 0 cos 2 φ v θ u + cos φ φ φ φ 0 cos φ v θ 0 2 cos 2 φ φ 0v u cos 2 φ cos 2 0 cos 2 φ v θ u + u φ φ 0 cos 2 φ v θ φ 0 2 cos 2 φ φ 0v u cos 2 φ cos 2 0 cos 2 φ v θ φ φ 0 2 cos 2 0 v φ φ u cos 2 φ + 0 cos 2 φ v θ u { } 0 2 cos 2 0 cos 2 u v φ θ v φ φ u cos φf 0 2 cos 2 φ φ φ u u.3 f 0 cos φ 0 0 cos φw u + 0 cos φ 0 { } 0 cos φ 0 cos φ f v θ w u v θ u φ + sin φu v θ cos φ { 0 cos φ 0 cos φ f v θ cos φ u } v sin φu θ w φ u cos φ { } 0 cos φ 0 cos φ f v θ u cos φ v θ w φ u cos φ { } u cos φ φ v 0 cos φ 0 cos φ f θ w cos φ u Fz 0 cos φ u φ + sin φu 0 v θ 2005/02/9

19 NumRu::GPhys::EP Flux 8,.3. u t + v cos φ φ u t + v cos φ φ u cos φ + w u fv X u cos φ + w u fv X,. 0 2 cos 2 φ φ 0 cos φ F. cos φf F φ + z 0 cos φ, F cos φf φ + F z cos φ φ A.7. A.2 A.3, A.3 t + v + v 0 0 φ + w cos φ φ cos φ φ v θ cos φ 0 0w θ, + w Q v 0 0 φ + cos φ φ t + v φ cos φ φ v θ cos φ 0 0w θ Q 2005/02/9

20 NumRu::GPhys::EP Flux 9. v 0 0 φ + cos φ φ cos φ φ v θ cos φ 0 0w θ v 0 0 φ φ cos φ φ + v θ cos φv θ + cos φv θ φ cos φ φ v θ cos φ 0 0w θ v 0 + v θ φ φ + v θ φ 0 0w θ v 0 φ + 0w θ + v θ φ + φ v θ 0 φ + w θ + v θ φ v 0 φ + w θ,. t + v + w φ Q 0. v 0 φ + w θ. 2005/02/9

21 NumRu::GPhys::EP Flux 20 v. A.2 A.3, A.3 v + v t v + v 0 0 v + v φ w v + v cos φ φ fu + tn φ u2 + Φ φ Y cos φ φ v 2 cos φ 0 tn φ 0v w u 2, fu + tn φ u2 + Φ φ v + v t 0 0 v + v 0 0 v + φ 0 w v + v cos φ φ 0 0 cos φ φ v 2 cos φ 0 tn φ 0v w u 2 + Y Andrews et l. 987,. G v. u f + tn φ u + Φ φ G. v 0,. 2005/02/9

22 NumRu::GPhys::EP Flux 2 u t + v cos φ φ u f + u tn φ u cos φ f + w u X 0 cos φ F, + Φ φ G. A.8 A.8b Φ Re κz/h θ 0. H cos φ φ v cos φ + 0 0w 0. A.8c A.8d t + v + w φ Q 0 0 v θ φ + w θ. A.8e 2005/02/9

23 NumRu::GPhys::EP Flux 22 D.G. Andrews, J.R. Holton, nd C.B. Leovy. Middle tmosphere dynmics, Interntionl Geophysics Series. Acdemic Press, J.R. Holton. The Dynmic Meteorology of the Strtosphere nd Mesosphere, Americn Meteorologicl Society, /02/9

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