, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. main.tex 2011/08/13( )

81 4 2 4.1, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,.

82 4.2. ζ t + V (ζ + βy) = 0 (4.2.1), V = 0 (4.2.2). (4.2.1), (3.3.66) R 1 Φ / Z, Γ., F 1 ( 3.2 ). 7,., ( )., (4.2.1) 500 hpa., 500 hpa (4.2.1) 1949,., U = U(y).. ζ = ζ(y) + ζ, u = U(y) + u v = v, ζ = dū/dy. (4.2.1), ζ t + U ζ ( ) x + ζ v y + β = 0 (4.2.3). ψ, u = ψ/ y, v = ψ/ x., (4.2.2)., (4.2.3) t 2 ψ + U x 2 ψ + ( ) β d2 U ψ dy 2 x = 0 (4.2.4)., ψ = Ψ(y) e ik(x ct) ( ). (4.2.4), ( ) ( ) d 2 Ψ d 2 (U c) dy U 2 k2 Ψ dy β Ψ = 0 (4.2.5) 2

83., y = 0, (y = ±d)., v(±d) = ψ x = ik Ψ(±d) e ik(x ct) = 0 y=±d., Ψ(d) = Ψ( d) = 0 (4.2.6),. (4.2.6) (4.2.5), c. U = U(y), U., (4.2.5) ( d 2 Ψ dy k 2 β ) Ψ = 0 (4.2.7) 2 U c. (4.2.6),. [ ] (2n 1)πy Ψ n = A cos n = 1, 2,... (4.2.8) 2d, [(2n 1)π/2d] 2 = k 2 + β/(u c)., c = U β k 2 + [(2n 1)π/2d] 2 (4.2.9)., 2.5. (4.2.8) Ψ n,. n = 1, d, c = U β/k 2 (4.2.10)., q/ y (2.6.53), (2.6.52). 2, (2.6.52) (2.6.53) (4.2.10)., (2.6.52) L *1., U k q *1 (2.6.52) (2.6.53) c = U β + U/L2 R k 2 (1 + L 2 /L 2 R ) (4.2.11)., L R = (gh) 1/2 /f, L = k 1. U 10 m, L R L 10 6 m, (4.2.10).

84 ((2.6.52) ). q = (f + ζ)/h 0 = f/h 0 (H 0 ), q.,, (4.2.10). (4.2.10) Rossby(1939),, (Hough, 1898). U > 0 λ = λ s = 2π(U/β) 1/2,. L < λ s, L > λ s. 500 hpa (4.2.10), (4.2.10). 4.3,. ψ = Ψ(y)e ik(x ct),. c = c r + ic i, Ψ., (4.2.5) Ψ (Ψ ), ) (U c) ( Ψ d2 Ψ dy 2 k2 Ψ Ψ ( d 2 U dy 2 β., Ψ d2 Ψ dy = d ( Ψ dψ ) dψ 2 dy dy dy ) Ψ Ψ = 0 (4.3.12)., 2. ΨΨ = Ψ 2 and dψ dψ dy dy = dψ dy, (4.3.12) U c ±d [ d ( d Ψ dψ ) k 2 Ψ 2 dψ 2] d dy dy dy dy (4.3.13) d (d 2 U/dy 2 β) Ψ 2 = dy U c. Ψ(±d) = 0, Ψ(±d)., Ψ Ψ, d dψ dy

85 1. (U c) = (U c r )+ic i, [ d k 2 Ψ 2 + dψ 2] d (d 2 U/dy 2 β)(u c r ) Ψ 2 dy = dy d dy d U c 2 (4.3.14) d (d 2 U/dy 2 β) Ψ 2 ic i dy U c 2 d. 1,, i. c i d d (d 2 U/dy 2 β) Ψ 2 U c 2 dy = 0 (4.3.15) c i 0, c i., d 2 U/dy 2 β d < y < d., y ( y k ) ( ) d 2 U dy β = 0 d < y 2 k < d (4.3.16) y k. Lord Rayleigh(1880), H.L.Kuo(1951),. (4.3.16). d dy ( du dy + f) = 0 or dζ a dy = 0 at y = y k (4.3.17),,.,. (4.2.4) ψ, x, y d [ ψ ψ Uψ t x 2 ψ ( ) ( )] ψ 2 β d2 U dy = 0 (4.3.18) x 2 dy 2 d., ( ) = L 1 L ( ) dx., 0., ψ(x + L, y, t) = ψ(x, y, t) (4.3.19) ψ(x, d, t) = ψ(x, d, t) = 0 (4.3.20)

86. (4.3.18), (4.3.19), *2. d d u 2 + v 2 dt d 2 d dy = u v d du dy dy (4.3.21), u = ψ/ y, v = ψ/ x., ψ. ψ(x, y, t) = Φ(y, t) cos[kx θ(y, t)] (4.3.22), Φ, θ. u v. u v = ψ ψ y x = Ψ 2 θ y k sin2 (kx θ) + k Ψ Ψ sin(kx θ) cos(kx θ) y (4.3.23), L 2π/k, u v = k θ Ψ2 (4.3.24) 2 y., u v θ/ y. (4.3.24), (4.3.21) d d u 2 + v 2 dt d 2 dy = k 2 d d Ψ 2 θ du y dy dy (4.3.25), ( θ/ y)(du/dy) < 0 ( ), ( θ/ y)(du/dy) > 0 ( ). 4.4, 2. U = U 0 sech 2 (y/y 0 ), (4.4.26) *2 : (4.3.21).

87 U = U 0 tanh 2 (y/y 0 ) (4.4.27). (4.4.26), Bickley. 4.4.1 4.4.2. (4.4.26) (U 0 > 0),. (U 0 < 0), (4.4.27). 4.4.1 4.4.2 d 2 U/dy 2, β = 0, (4.3.16)., ( ) ( ) d 2 U d 2 U > β and < β (4.4.28) dy 2 dy 2 max. U 3 (d 2 U/dy 2 ) max (d 2 U/dy 2 ) min, 2 4.4.1 4.4.2. Bickley, min 2 < b < 2/3 (4.4.29) 4.4.1: U = U 0 sech 2 y/y 0 4.4.2: U = U 0 tanh y/y 0

88., b = βy 2 0/U 0 (4.4.30)., b < 4/(3 3) (4.4.31). (4.4.26) (4.4.27) (4.2.5), b ky 0. Kuo(1973), (4.2.5), (4.2.6) c (4.4.26) (4.4.27). 4.4.3, Kuo(1973), (d ) Bickley (4.4.26) c r /U 0 δ = ky 0 c i /U 0. b > 0, b < 0. 4.4.3 (a). (b > 0), U 0 50%., (b < 0), U 0 2.5. ((4.2.11) ), b (k 0), c r. 4.4.3 (b), 2 < b < 2/3. β,., (b )., b. 4.4.4, (4.4.27) (Kuo(1973) ). (4.4.31),. 4.4.4 (a), c r = 0 b = 0,. c r U 0 90%, b c r. 4.4.4 (b), b = 0, b = 4/(3 3)., b. Bickley.,.., Williams et al(1971) U 0 > 0, b = 0, d = 5y 0. 4.4.5, Bickley (ky 0 = 0.9)

89 4.4.3: Kuo(1973) U = U 0 sech 2 (y/y 0 ). (a)ky 0 c r /U 0 b ; (b)b ky 0 δ. (H.L.Kuo, Dynamics of Quasi-geostrophic Flows. Academic Press, 1973.)

90 4.4.4: Kuo(1973) U = U 0 tanh (y/y 0 ). (a)b ky 0 c r / U 0 ; (b)b ky 0 δ. (H.L.Kuo, Dynamics of Quasi-geostrophic Flows. Academic Press, 1973.)

91 4.4.5: Bickley. (a) P ; (b) θ ( ). (Haltiner,G.J., Williams,R.T., 1979 : NUMER- ICAL PREDICTION AND DYNAMIC METEOROLOGY SECOND EDITION. John Wiley & Sons, 477pp). ψ = P (y) cos(k(x c r t) θ(y)), P (y), θ. y = 0,., (4.5).,. 4.4.6, U 0 > 0, b = 0 (ky 0 = 0.45)., y = ±y 0, y = 0., ( ).

92 4.4.6: (4.4.27) 4.4.5. (Haltiner,G.J., Williams,R.T., 1979 : NUMERICAL PREDICTION AND DYNAMIC METE- OROLOGY SECOND EDITION. John Wiley & Sons, 477pp) 4.5,.,., β = 0, (4.2.6) (4.2.5).,. (4.2.3) (β ), U = U 0 + Sy., (4.2.4) 2 ψ t.. + U 2 ψ x = 0 (4.5.32) 2 ψ = F (x Ut) (4.5.33), F, F (x) t = 0.,. v = v 0 sin kx

93,, t 2 ψ = ζ = kv 0 cos kx at t = 0 2 ψ = kv 0 cos k(x Ut) (4.5.34).,., ψ = A cos k(x Ut),. 2 ψ = Ak 2 cos k(x Ut) AS 2 t 2 k 2 cos k(x Ut) (4.5.34) A.,., ψ = v 0 cos k(x Ut) k(1 + S 2 t 2 ) u = U ψ y = U v 0kSt sin k(x Ut) k(1 + S 2 t 2 ) v = ψ x = v 0 sin k(x Ut) 1 + S 2 t 2 (4.5.35). ψ v t 2, u t. U = U 0 + Sy,.,.,., y = y, c(y ) = U(y )..,.,,., (4.2.8),. Case(1960), (4.2.5) (4.2.6),.,,.,,,.

94 4.6,,.,., (Case, 1960).,,. -,., u v.,,,,.,,.,.,, ( ).

95 4.7,., Charney(1947) Eady(1949).,., (3.3.66). ( ) t + k ψ q = 0 (4.7.36), q q = 2 ψ + e Z ( f 2 0 e Z Z Γ ) ψ + βy (4.7.37) Z, (potential vorticity)., ψ = f0 1 Φ, Γ (3.3.47) *3., (3.3.55) ( ) ψ t + k ψ Z + f 0 1 ΓŻ = 0 (4.7.38). Z, T/ z Γ., Z., *4,. ψ,. ψ (x, y, Z, t) = ψ(y, z) + ψ(x, y, Z, t) (4.7.39), ψ / ψ., U = ψ/ y. (4.7.36) (4.7.39), ( t + U ) q + ψ q x x y = 0 (4.7.40) *3 (3.3.47). Z, Γ(Z) = ( ) ( ) ( Φ Z Z + κ Φ T = R Z + κ T = H2 g g + 1 T ) T c p H Z. *4 σ(p),. σ(p) = Γ/p 2

96., q = 2 ψ + e Z ( f 2 0 e Z ψ Z Γ Z q y = β 2 U y ( f 2 0 e Z 2 ez Z Γ ), (4.7.41) ) U Z (4.7.42). (4.7.42) ( 2 ) ( 3 )., ( t + U ) ψ x Z ψ U x Z + f 0 1 ΓŻ = 0 (4.7.43)., Ż.,. ψ = Ψ(y, Z)e ik(x ct), (4.7.40) [ 2 Ψ (U c) y + ( ) ] f 2 0 e Z Ψ 2 ez k 2 Ψ Z Γ Z., + q y Ψ = 0 (4.7.44) (U c) Ψ Z U Z Ψ ik 1 f 1 0 ΓW = 0 (4.7.45)., Ż = W (y, Z)e ik(x ct). Charney and Stern(1962) Pedlosky(1964a), (4.3.16)., q/ y U/ Z. 3, (4.3.16), (Holton, 1975 ). 4.8 Eady, Eady(1949).. β = 0 (e Z const)

97 (Γ = const) y ( / y = 0) rigid-lid(w = 0 at Z = 1), Z U = SZ (4.8.46)., S.,., e Z, Γ, (4.7.44) (U c) ( f 2 0 Γ ) d 2 Ψ dz 2 k2 Ψ = 0 (4.8.47). U c 0,. ( ) ( ) Z Z Ψ = A sinh + B cosh ε 1/2 ε 1/2 (4.8.48), ε = f 2 0 /k 2 Γ ((3.3.48) ). Z = 0, 1 W = 0, (4.7.45), (U c) dψ dz SΨ = 0 at Z = 0, 1 (4.8.49). (4.8.48) Z, (4.8.49) cε 1/2 A SB = 0, (S c)ε 1/2 [A cosh(ε 1/2 ) + B sinh(ε 1/2 )] S[A sinh(ε 1/2 ) + B cosh(ε 1/2 )] = 0 (4.8.50). A, B,.,. c 2 Sc + S 2 (ε 1/2 coth ε 1/2 ε) = 0 (4.8.51) c, c = S 2 ± S [ 1/4 (ε 1/2 coth ε 1/2 ε) ] 1/2 = S {[ ( )] [ ε 1/2 ε 1/2 ε 1/2 2 ± Sε1/2 tanh 2 2 2 ( )]} ε 1/2 1/2 (4.8.52) coth 2

98., ε 1/2 < 1.20 (4.8.53) 2,. c,. (3.3.48) ε = L 2 /L 2 R ( L R = Γ 1/2 /f 0 ), (4.8.53). λ 2π = L > L R 2.40, kc i = ± S {[ ( )] [ ( ) ]} ε 1/2 ε 1/2 ε 1/2 tanh coth ε 1/2 L R 2 2 2 2 (4.8.54) (4.8.55)., S., L (4.9), S 0. L, L = L R (4.8.56) 1.61., L L R ε 1. ε 1,., c r = S 2 (4.8.57),. Z = 1/2, Z = 1/2 *5.,. *5, Eady.,. (4.8.50), (4.8.48) B, Ψ(Z) Ψ = A [{ sinh ( Z ε ) c r S ε cosh ( Z ε )} c i i S ε cosh ( Z ε., Ψ Ψ kθ (, Ψ(Z) = Ψ(Z) e kθ ). ( ) Z Ψ(Z) 2 = A {sinh 2 c ( )} 2 ( ) r Z ε S ε cosh + A 2 c2 i Z ε S 2 ε cosh2 ε tan kθ = c ( ) [ ( ) i Z Z S ε cosh sinh c ( )] 1 r Z ε ε S ε cosh ε. A. )]

99, (4.8.49). Ψ = 0,. Eady,., k 1. Pedlosky(1964b),. Charney Charney(1947) Eady, Eady. Charney,.,., (4.7.42), q y = β + f 2 0 S/Γ (4.8.59), Γ. (S > 0),., Eady., (4.7.44). (SZ c) [ f 2 0 Γ ( d 2 Ψ dz dψ 2 dz ) ] k 2 Ψ + (β + f 0 2 S )Ψ = 0 (4.8.60) Γ q/ y, (4.8.47).,., r = Γ(β + Sf 2 0 /Γ) f 2 0 S(1 + 4Γf 2 0 k 2 ) 1/2 (4.8.61)., c. Gambo(1950), Kuo(1952), Green(1960), Burger(1962), Kuo(1973). 4.8.7,, ψ, ψ(x, Z, t) = Ψ(Z) e kc it exp [ik(x c r t + θ(z))] (4.8.58). (4.8.53), Ψ θ, Z = 1/2, Z = 1/2.

100 4.8.7: Green(1960) Charney., Z = 1. (Green, J.S.A, 1960 : A Problem in Baroclinic Stability. Royal Meteorological Socitey) Green(1960), Z = 1. 1/k, S., kc i. ( ), r = 1 Charney, Gambo, Kuo.. Burger, r, r. 2, r = 2, 3.,., 0.1,. S, Eady.

101 4.9 2 Charney,. 2 4.9.8 4, 1,3, 2. 2, Charney.,. (3.3.76) (3.3.77). 4.9.8: 2

102 ( ) t + k ψ ( 2 ψ ω + βy) f 0 p = 0 (4.9.62) ( ) ψ t + k ψ p + σ ω = 0 (4.9.63) f 0 2, (4.9.62) (4.9.63), 2.,. (4.9.62) (4.9.63),. ψ = U(p)y + ψ(x, p, t) ω = ω (x, p, t) (4.9.64), U(p) y. (4.9.64) (4.9.62) (4.9.63), ( t + U ) 2 ψ x x + β ψ 2 x f ω 0 p = 0 (4.9.65) ( t + U ) ψ x p du ψ dp x σ ω = 0 (4.9.66) f 0. (4.9.64), ψ ω. p = p s p = p T ω = 0. p = p T,,., (4.9.65) 1, 3, ( ) t + U 2 ψ 1 1 x x + β ψ 1 2 x f ω 0 p = 0 (4.9.67) ( ) t + U 2 ψ 3 3 x x + β ψ 3 2 x + f ω 0 p = 0 (4.9.68) (4.9.69)., (4.9.66) 2., 2 ψ U 1,3 ψ U, [ t + ( ) ] U1 + U 3 (ψ 1 ψ 3 ) 2 x ( U1 U 3 2 ) ( ψ1 x + ψ 3 x ) ( pσ2 f 0 ) ω 2 = 0 (4.9.70)

103. (4.9.67), (4.9.68), (4.9.70), 3 ψ 1, ψ 3, ω 2.,. (4.9.67) ψ 1, (4.9.68) ψ 3 2, x, [ ] d ( ψ1 / x) 2 + ( ψ 3 / x) 2 dt 2 = f 0 p ω 2(ψ 1 ψ 3 ) (4.9.71).., (4.9.70) λ(ψ 1 ψ 3 ), x. [ ] d λ(ψ1 ψ 3 ) 2 dt 4 = λ ( 4 (U ψ1 1 U 3 ) (ψ 1 ψ 3 ) x + ψ ) 3 x + f 0 p ω 2(ψ 1 ψ 3 ) (4.9.72), λ = 2f 2 0 /( p 2 σ 2 ) (4.9.73). ψ 1 ψ 3, *6. (4.9.72),. 1.11 *6, Φ p = RT p., Φ. Φ = Φ(p) + Φ (x, p, t), Φ p = RT p., Φ = f 0 ψ. 1 3, T 2 = f 0 ψ 1 ψ 3 R ln(p 3 /p 1 )., 2 T 2 1 3. p3 T p 2 = 1 (T/p) dp p3 (4.9.74) dlnp p 1, ψ 1 ψ 3, 1 3 T 2.

104,. (4.9.71), (4.9.72) 2,., 2 (ψ 1 ψ 3 > 0) (ω 2 < 0), (ψ 1 ψ 3 < 0) (ω 2 > 0).,. U 1 U 3,. (4.9.72) 1, (U 1 U 3 )., 2 (( ψ 1 / x + ψ 3 / x)/2 > 0) (ψ 1 ψ 3 > 0), (( ψ 1 / x + ψ 3 / x)/2 < 0) (ψ 1 ψ 3 < 0),., U 1 U 3.,. ψ 1 = Ψ 1 e ik(x ct) ψ 3 = Ψ 3 e ik(x ct) (4.9.75) ω 2 = ( pf0 1 )W e ik(x ct) (4.9.67), (4.9.68), (4.9.70), k[β k 2 (U 1 c)]ψ 1 + iw = 0 k[β k 2 (U 3 c)]ψ 3 iw = 0 k[u 3 c]ψ 1 k[u 1 c]ψ 3 + i2w/λ = 0 (4.9.76a) (4.9.76b) (4.9.76c). Ψ 1, Ψ 3, W,. c 2. 2k 2 (k 2 + λ)c 2 + [2β(2k 2 + λ) 2k 2 (k 2 + λ)(u 1 + U 3 )]c + 2β 2 β(2k 2 + λ)(u 1 + U 3 ) + 2k 4 U 1 U 3 + k 2 λ(u 2 1 + U 2 3 ) = 0 2 c, c = (U 1 + U 3 )/2 β(2k2 + λ) 2k 2 (k 2 + λ) ± [λ2 β 2 k 4 (λ 2 k 4 )(U 1 U 3 ) 2 ] 1/2 2k 2 (k 2 + λ) (4.9.77). (4.9.77) c,., k 4 λ 2 (U 1 U 3 ) 2

105. c,. (k 1 ) (U 1 U 3 ),.. (U 1 U 3 ) 2 λ 2 β 2 = (4.9.78) k 4 (λ 2 k 4 ) λ β,, 4.9.9 n = 0.,. k 1 = λ 1/2 = pσ 1/2 2 /(f 0 / 2) (4.9.79) 4.9.9: λ = 5.88 10 12 m 2, β = 1.67 10 11 m 2 s 1 2 n = k c i. n U 1 U 3 k 1., k 1, U 1 U 3, n 10 6 m, ms 1, 10 5 s 1.

106, k 2 λ, (4.9.78). U 1 U 3 = β/k 2 (4.9.80), (4.9.78). (4.9.78) k 1, k 1 = 2 1/4 λ 1/2, U 1 U 3 (U 1 U 3 ) min = 2β/λ = β p2 σ 2 f 2 0 (4.9.81). 2 (two level model),, 2 2 (two layer model)(phillips, 1951). (4.9.79),.,, (4.9.80),., β.,,., β = 0 k 1 > σ 1/2 2 /(f 0 2) U1 U 3 (4.9.82)., Eady k 1 > Γ/(f 0 2.4) S = du/dz 0 (4.9.83).,. β 0, 2 ( 4.9.9), Charney ( 4.8.7).,,.,.,., 4.8.7., 4.9.9 2 (4.9.78)., 2., 4000 5000 km.

107 4.10 2 2., (4.9.71) (4.9.72). (4.9.77) 2, c +, c. 2.6,, ( ). 2, [ ] ψ 1 = Re ψ 3 = Re ω 2 = pf 1 0 Re a + Ψ + 1 e ik(x c+ t) + a Ψ 1 e ik(x c t) [ a + Ψ + 3 e ik(x c+ t) + a Ψ 3 e ik(x c t) [ a + W + e ik(x c+ t) + a W e ik(x c t) ] ] (4.10.84a) (4.10.84b) (4.10.84c)., Re. ψ = Ψ e iθ, (4.10.84) e ix = cos x + i sin x (4.10.85). ω 2, ψ 1 ψ 3, (4.10.84c). c + c, (4.9.76). (4.9.76a) (4.9.76b), Ψ ± 1 = c± (U 3 β/k 2 ) c ± (U 1 β/k 2 ) Ψ± 3 (4.10.86)., (4.9.76b). W ± = ik 3 [c ± (U 3 β/k 2 )]Ψ ± 3 (4.10.87) ψ 1 ψ 3, a + a (4.10.84a) (4.10.84b). 4.9.9, c ±, c + > c., (4.10.86), Ψ ± 1 Ψ± 3 180., (4.10.87), 90.

108, (4.9.71) (4.9.72), *7. (4.10.84) 2,., (4.9.77) β/k 2., (4.9.77) c ± = U 1 + U 3 2 ± 1 2 [ ] k 2 1/2 λ k 2 + λ (U 1 U 3 ) 2 (4.10.88)., (4.10.86) Ψ + 1 /Ψ + 3 > 1, Ψ 1 /Ψ 3 < 1 (4.10.89).,,. W = W e iθ (θ ), Ψ 3 > 0, (4.10.87) (4.10.88) θ = π/2., (ω < 0), (ω > 0)., 4.8 Eady.,. U 1 U 3, (4.9.77) c + = (U 1 + U 3 )/2 β/(k 2 + λ) c = (U 1 + U 3 )/2 β/k 2 (4.10.90). c, (4.10.86) (4.10.87) W = 0 Ψ 1 = Ψ 3, ((4.2.10) )., c +, (4.10.86) (4.10.87) W 0 Ψ + 1 = Ψ + 3,., (U 1 U 3 ) 2,. 4.9.9,. c ± = c r ± in/k *7 Ψ + 1 Ψ+ 3 ( Ψ 1 Ψ 3 ) 180, Ψ+ 1 Ψ 3 ( Ψ 1 Ψ+ 3 )., Ψ+ 1, Ψ+ 3 W ( Ψ 1, Ψ 3 W + ) 90. (4.10.84) 2,.

109, c r = (U 1 + U 3 )/2 β(2k 2 + λ)/[2k 2 (k 2 + λ)] n = [k 4 (λ 2 k 2 )(U 1 U 3 ) 2 λ 2 β 2 ] 1/2 /[2k(k 2 + λ)] (4.10.91), n., ψ 1,3 = Re [ a + Ψ + 1,3e ik(x crt) e nt + a Ψ 1,3e ik(x crt) e nt] (4.10.92). a + = 0,,.,. c, (4.10.86) (4.10.87),. (4.10.91), (4.10.86) (4.10.87). Ψ ± 1 = {c r [(U 1 + U 3 )/2 β/k 2 ]} 2 (U 1 U 3 ) 2 /4 + n 2 /k 2 in(u 1 U 3 )/k [c r (U 1 β/k 2 )] 2 + n 2 /k 2 Ψ ± 3 (4.10.93) W ± = k 3 {±n/k i[c r (U 3 β/k 2 )]}Ψ ± 3 (4.10.94) (4.10.93),. 2, *6. T 2 = f 0 (ψ 1 ψ 3 )/[R ln(p 3 /p 1 )] (4.10.95),. f 0 = 10 4 s 1, β = 1.67 10 11 m 1 s 1, 2π/k = 4000 km, λ = 5.88 10 12 m 2, p s = 1000hPa, p = 400hPa, U 1 U 3 = 20 ms 1, a = 0, a + Ψ + 3 = 10 ms 1 /k, 3. (4.10.93), (4.10.92) ψ 1 ψ 3. ψ 1 = (14.2 ms 1 )k 1 cos[k(x c r t) + 64 ] e nt ψ 3 = (10 ms 1 )k 1 cos[k(x c r t)] e nt (4.10.96),, (4.10.84c), (4.10.94). ω 2 = 1.36 10 3 hpa s 1 cos[k(x c r t) + 116 ] e nt (4.10.97)

110, ψ 1, ψ 3 (4.10.95), T 2 = (4.24 K) cos[k(x c r t) + 108 ] e nt (4.10.98)., y k. (4.10.96), (4.10.97), (4.10.98), 4.10.10 4.10.10: (4.10.96), (4.10.97), (4.10.98).

111. ψ 1 ψ 3, T, R.., (4.10.96) 1, *8., W C.,,.,., 2.,.,,. 4.10.10,,. (4.9.71) (4.9.72), 4.10.10 (4.10.96), (4.10.97), (4.10.98).,,,.,.,.,. Oort(1964),. 4.10.11., K, P., K ( ), P.,. { P P }, {P K }, (4.9.72), (4.9.71)., {K K} (4.3.21). { P K ω T,. 4.10.11, Q P, P K.,.,,,. K K *8 β = 0, (4.10.93) 1.

112 4.10.11: Oort(1964).,. 10 5 J m 2., Wm 2. (Oort, A.H., 1964: On Estimates of the Atmospheric Energy Cycle., American Meteorological Society )

113, 4.6. P K.,.,.,,.,,.,. (4.9.62), (, ) ( ω/ p > 0),.,.,. Eady Charney,. Gall(1976), Simmons and Hoskins(1977),., 2000 km.,, 4000 km.,. Staley and Gall(1977),. Gall, etal(1979),.,.

114 4.11 8,.,,. (2.4.11), ρ 1/2,.,,.,.,., Eliassen and Palm(1960), Charney and Drazin(1961). c, (4.7.43), (U c) 2 ψ x Z ψ U x Z + f 0 1 ΓŻ = 0 (4.11.99)., ψ x, ψż = f 0Γ 1 (U c) ψ ψ x Z (4.11.100). ψ Φ,., ψ/ x ψ/ Z. (4.11.100),,.,. U(Z),., Charney and Drazin(1961), (4.7.40). U y, ψ = Ψ(Z) cos αy e ik(x ct) (4.7.40), [ (U c) e Z ( ) ] f 2 0 e Z Ψ (k 2 + α 2 )Ψ + q Z Γ Z y Ψ = 0 (4.11.101)

115.,., q y = β ( ) f 2 0 e Z U ez Z Γ Z Q = f 0 (e Z /Γ) 1/2 Ψ (4.11.102), (4.11.101)., (4.11.101)., d 2 Q dz 2 + n2 Q = 0. (4.11.103) n 2 = Γ f 2 0 (k 2 + α 2 ) Γ 1/2 Z/2 d2 e dz 2 (e Z/2 Γ 1/2 Γ q/ y ) + f0 2 (U c) (4.11.104). (4.11.103), n(z).,. n 2 > 0 : Q(Z) Z,. n 2 < 0 : Q(Z) Z,., U Γ,., (4.11.104), n 2 = Γ [ k 2 + α 2 + f ] 0 2 f0 2 4Γ β (4.11.105) (U c), n 2., (4.11.103) e inz e inz. n,, e Z/2 ((4.11.102) ). n, e n Z e n Z.,, (e n Z ). Charney and Drazin(1961),, (4.11.105). (4.11.105) c = 0, (n 2 > 0), 0 < U < β k 2 + α 2 + f 2 0 /4Γ (4.11.106)

116.,,,.,, (4.11.106) 38 m/s.. (4.11.106), U Z,.,,., Matsuno(1970),,. (4.11.106) ( k),. Charney and Pedlosky(1963),. Holton(1975),.,., 7 10.

117 4.12,.,.,.,., Matsuno(1966a).,, (f = βy).,., φ = gh, Φ = gh. u t + φ βyv = 0, x v t + φ + βyu = 0, (4.12.107) y ( φ u + Φ x + v ) = 0. y