62 3 3.1,,.,. J. Charney, 1948., Burger(1958) Phillips(1963),.,. L : ( 1/4) T : ( 1/4) V :,. v x u x V L, etc, u V T,,.,., ( )., 2.1.1.
63 3.2,.,.,. (2.6.38a), (2.6.38b), V + V V + Φ + fk V = 0 (3.2.1)., Φ = gh, f.,. (2.6.40), Φ + V Φ + Φ V = 0 (3.2.2). T = L/C (3.2.3), C. C V, T = L/V (3.2.4).,. L 10 6 m, V 10 m/s, T 10 5 s ( 1 )., 1/4. (3.2.1). V + V V + Φ + fk V = 0 (3.2.5) R o fv R o fv fv, R o = V/fL.., f 10 4 s 1, L 10 6 m, V 10 m/s, R o 0.1.,.
64 R o, (3.2.5).,., Φ fv (3.2.6) (3.2.2), Φ. Φ = Φ + Φ (3.2.7), Φ = gh. Φ, (3.2.6). Φ fv L (3.2.8),. (3.2.7) (3.2.2), (3.2.4) (3.2.8), Φ + V Φ + Φ V + Φ V = 0 (3.2.9) R o F Φ V L R o F Φ V L R o F Φ V L ΦV/L., F = f 2 L 2 / Φ (rotational Froude number).. F = f 2 L 2 / Φ = L 2 /L 2 R (3.2.10), L R = Φ 1/2 /f (Rossby radius of deformation). 2.7, L R. R o, (3.2.5) Φ + fk V = 0 or V = f 1 k Φ (3.2.11)., R o. F 1, (3.2.9) Φ V = 0 (3.2.12). f, (3.2.12) (3.2.11). (3.2.11) (3.2.12)
65,.,., (3.2.11), (3.2.12), ( 2.7 )., Richardson(1922) (3.2.9),,., (3.2.1) (3.2.2) ( 2.5 ).. 2.5,., R o 1 1 (3.2.11), (3.2.12)., *1. V = V ψ + V χ, V ψ = k ψ, V χ = χ (3.2.13), ψ, χ., ζ = k V = 2 ψ D = V = 2 χ (3.2.14)., ψ χ., (3.2.1) k. + V ζ + (f + ζ) V = 0 (3.2.15), (3.2.1).. D + (V V ) + 2 Φ fζ = 0 (3.2.16) V ψ V, V χ R 1 V (3.2.17) *1, 3 F, 0, F., F = φ + A, φ, A.,.
66, R 1. (3.2.13) (3.2.9), (3.2.17) Φ + V ψ Φ + V χ Φ + Φ V χ + Φ V χ = 0 (3.2.18) R o F Φ V L R of Φ V L R 1 R o F Φ V L R 1R o F Φ V L R 1 Φ V L. *2, R 1 R o F (3.2.19)., (3.2.13) (3.2.15),, + V ψ ζ + V χ ζ + fd + ζd = 0 V 2 L 2 V 2 L 2 R 1 V 2 R 1 V 2 V 2 R L 2 R o L 2 1 L 2 (3.2.20)., ζ V/L, D R 1 V/L. (3.2.16), D + (V ψ V ψ ) + (V ψ V χ ) + (V χ V ψ ) R 1 V 2 L 2 V 2 L 2 R 1 V 2 V 2 R L 2 1 L 2 (3.2.21) + (V χ V χ ) + 2 Φ fζ = 0 R1 2 V 2 1 V 2 1 V 2 L 2 R o L 2 R o L 2. (3.2.20),., R 1 R o (3.2.22) D ζ = R 1 (3.2.23)., R 1 (3.2.19) (3.2.22)., L = k 1, Φ = gh, (2.6.61).,. *2.
67 F 1, R o 1., (3.2.19) (3.2.22) R 1 = R 0. (3.2.9), (3.2.20), (3.2.21), R o,. Φ + V ψ Φ + ΦD = 0 (3.2.24) + V ψ ζ + fd = 0 (3.2.25) 2 Φ fζ = 0 (3.2.26) (3.2.26), ζ = 2 ψ, ψ = Φ /f., V ψ = k ψ = f 1 k Φ (3.2.27). (3.2.11). (3.2.24), (3.2.25), (3.2.26)( (3.2.27)), (quasi-geostrophic equation)., ( ). (3.2.23), (3.2.24) (3.2.25). (3.2.24) (3.2.25) D, ( ) + V ψ (ζ f ΦΦ ) = 0 (3.2.28)., (quasi-geostrophic potential vorticity equation). (2.6.42), (2.6.42), *3. (3.2.26) (3.2.27), (3.2.28) Φ. *3,. q = f + ζ 1 f + ζ = g Φ h + H 1 + (Φ / Φ) g Φ 1 f g Φ [ ] 1 f 1 + (ζ/f) (Φ / Φ) [ ] 1 + (ζ/f))(1 (Φ / Φ), h/h 1., R 1 (= R o ) 1 ζ/f 1., V ψ V χ R 1 (= R o ), V ψ (3.2.28).
68, (3.2.24) (3.2.25) (3.2.26). ( 2 f ) 2 D = 1 Φ f Φ k Φ ( 2 Φ ) (3.2.29),., (2.6.59) x. (3.2.29), Φ (3.2.26).,., (L 10 6 m, f 10 4 s 1, Φ 1/2 = 300 m/s) F, F 0.1. F 1,. F R o 1, (3.2.19) R 1 = Ro 2. (3.2.20), + V ψ ζ = 0 (3.2.30).., (3.2.27). (3.2.28), (3.2.30),,. (3.2.1), (3.2.2),.
69 3.3,.. Z = ln(p/p 0 ) (3.3.31), p 0. Z, z, Φ = gz. RT = pα = p Φ p = Φ (3.3.32) Z, H = RT /g( 8 km) Z., T. 1,. p = p = 1 (3.3.33) p, ( 1.8 ). Ż, ω. Ż = ṗ/p = ω/p (3.3.34) Z, V + V V + Ż V., 1 (3.3.32), Φ + V Φ + Ż + Φ + fk V = 0 (3.3.35) ( ) Φ + κφ = κq (3.3.36)., κ = R/c p, Q., V + Ż Ż = 0 (3.3.37)., R o, ε, L/a., a. ε,
70. F,., V L, 1 L, 1 (3.3.38)., f β = 2Ω cos φ /a. β. Z, / 1 8 km ( )., V ψ V χ ((3.2.13) (3.2.14) )., Φ = Φ(Z) + Φ (3.3.39)., Φ(Z).. V ψ V, V χ R 1 V (3.3.40) Ż R 1 V/L (3.3.41) Φ fv L (3.3.42), R 1. Ż, V χ (3.3.37). Φ, (3.2.8).,., + V ψ ζ + V χ ζ + V ψ f + V χ f + Ż V 2 L 2 V 2 L 2 R 1 V 2 L 2 (βa/f)l/a R o V 2 L 2 (βa/f)l/a R o R 1 V 2 L 2 R 1 V 2 L 2 (3.3.43) + fd + ζd + k Ż V ψ + k Ż V χ = 0 R 1 V 2 R 1 V 2 R 1 V 2 R1V 2 2 R o L 2 L 2 L 2 L 2., ζ V/L, D R 1 V/L., R o = V/fL V 2 /L 2.
71, D + (V ψ V ψ ) + (V ψ V ψ + V χ V ψ ) R 1 V 2 V 2 R 1 V 2 L 2 L 2 L 2 R 2 1V 2 + (V χ V χ ) + Ż V ψ + Ż D L 2 L 2 L 2 R 1 V 2 R 1 V 2 + Ż V χ + 2 Φ fζ k f V ψ k f V χ = 0 R1V 2 2 1 V 2 1 V 2 (βa/f)l/a V 2 (βa/f)l/a R 1 V 2 L 2 R o L 2 R o L 2 R o L 2 R o L 2 (3.3.44). (3.3.37) Ż,. D + Ż Ż = 0 R 1 V L R 1 V L R 1 V L 1 (3.3.36),. Φ, + V ψ Φ + V χ Φ + ŻΓ(Z) ( Φ + Ż + κφ fv 2 fv 2 R 1 fv 2 R 1 fv 2 R o ε R 1 fv 2 Γ(Z) = ) = κq ( ) ( ) ( Φ + κ Φ T = R + κ T = H2 g g + 1 T ) T c p H (3.3.45) (3.3.46) (3.3.47). (3.3.47), (3.3.32) H = R T /g. Γ,. ε, ε f 2 L 2 Γ 1 (3.3.48).. ε = 1/(R 2 or i ) (3.3.49)
72, R i = Γ/V 2 (3.3.50).,., (3.3.46).,,. (3.3.48), (3.3.50). g 10 ms 2, T 300 K, g/cp + H 1 T / 3.5 10 3 Km 1, H 10 4 m, V 10 ms 1,. R i 100 (3.3.51) 3.3.1 L 10 6 m., R o 0.1, L/a 0.1, ε 1, βa/f 1., a 6.4 10 6 m, f 10 4 s 1. ε 1, (3.3.43) (3.3.46) R 1 R o (3.3.52)., R 1 = R o. (3.3.44), (3.3.43), (3.3.46) R o,. + V ψ (ζ + f) + fd = 0 (3.3.53) Φ + V ψ Φ 2 Φ fζ = 0 (3.3.54) + Γ(Z)Ż = 0 (3.3.55) (3.3.53),,, ζ,., (3.3.55),,.
73,., = i x + j, V = ui + vj (3.3.56) y, x, y. (3.3.53) (3.3.54) f,., V ψ f = v ψ df dy = v ψβ (3.3.57) β = d (2Ω sin φ) = 2Ω cos φdφ dy dy = 2Ω cos φ a (3.3.58). f, f y = y 0 [ f = f 0 + β 0 (y y 0 ) + = f 0 1 + β ] 0 (y y 0 ) +... (3.3.59) f 0. L, y y y 0 L. β f/a, (3.3.59) 2, β 0 (y y 0 ) f 0 L/a (3.3.60). L/a 0.1, f f = f 0, (3.3.57) β β 0.,,., L/a. Phillips(1963), Z,,.,., (3.3.53) D (3.3.45), (3.3.53) + V ψ (ζ + β 0 y) f 0 e Z (e Z Ż) = 0 (3.3.61)., (3.3.54)., 2 Φ = f 0 ζ = f 0 2 ψ (3.3.62) ψ = f 1 0 Φ (3.3.63)
74,. V ψ = f 1 0 k Φ, ζ = f 1 0 2 Φ (3.3.64) (3.3.55) (3.3.61) Ż, 1. (3.3.55) Ż, e Z Z, (e Z Ż) = ( e Z Γ Φ ) V ψ ( e Z Γ Φ ) (3.3.65)., V ψ /, (3.3.64). (3.3.61), ( ) [ + V ψ ζ + β 0 y + e Z ( )] f0 e Z Φ = 0 (3.3.66) Γ., (quasi-geostrophic potential vorticity equation), (3.2.28). (3.3.64), Φ. [ 2 + e Z ( f 2 0 e Z ) ] Φ Γ = k Φ [ f0 1 2 Φ + β 0 y + e Z ( e Z Γ )] (3.3.67) Φ,.,, (3.3.67) Φ /., Ż., (3.3.61) (3.3.55). = f 0 1 2 Φ R T = V ψ (ζ + β 0 y) + f 0 e Z (e Z Ż) (3.3.68) = Φ = V ψ Φ Γ(Z)Ż (3.3.69) V ψ (ζ + β 0 y) V ψ (Φ /), / T / Φ /. Ż, (3.3.68) Z, (3.3.69) f 0 2. ( Γ(Z) 2 Ż + f0 2 e Z ) (e Z Ż) (3.3.70) =f 0 [V ψ (ζ + β 0 y)] 2 [V ψ Φ ]
75, (quasi-geostrophic vertical motion equation)., (3.2.29). (3.3.64) Φ. Φ,, Ż. Ż (3.3.70), (3.3.45)., (3.3.68).,. (3.3.70),. Φ,, (3.3.70).,. (3.3.67) (3.3.70),. Ż, (3.3.67), (3.3.55) (/)(Φ /). (Z ), Ż.,, Ż w. gw = dφ/dt,. gw = Φ + V ψ Φ + V χ Φ + Ż Φ + ŻR T (3.3.71) fv 2 fv 2 R 1 fv 2 R 1 fv 2 R 1 MfV 2 R o, Φ/ = R T., M. M R T /f 2 L (3.3.72),., R 1 = R o, M 10., R T 10 5 m 2 s 2. 3.2, H f 2 L 2 /gh. H H = RT /g, M = F 1., (3.3.71), gw = R T Ż (3.3.73)., w g 1 fv 2 M 1 cms 1. (3.3.73) Z = Z s, Ż s = (g/r T )w S = (g/r T )V h s (3.3.74)
76, h s (x, y). (Charney and Eliassen, 1949), Phillips(1963)., (3.3.74) Żs = 0. Z s, Z s ( Z s = 0) (3.3.74) *4., p = p 0 (3.3.74). Z = 0, Z, Z s *5., H/10( 1 km),, 1/10.. (3.3.33) (3.3.34), (3.3.61) (3.3.55), ( ) + V ω ψ (ζ + β 0 y) f 0 p = 0 (3.3.76)., Φ p + V ψ Φ + σ(p)ω = 0 (3.3.77) p σ(p) = Γ/p 2 = p 1 d dp ( p Φ ) p Φ. (3.3.66),. ( ) [ + f 0 1 V Φ f0 1 2 Φ + β 0 y + ( )] f0 Φ = 0 (3.3.78) p σ(p) p *4 Z Z s, Z = Z s (3.3.74)., (Z s = 0)., Z s = 0. *5 T (x, y, Z, t) Z Z = 0, A(x, y, Z, t) = V (x, y, 0, t) + T Z +... Z=0, Z = Z s Z = 0 T (Z s ) T (Z) R 1 ( 2 Φ/ T (Z s) T (Z) 2 ) Z=0 T Z s (3.3.75)., / 1.
77, (3.3.70), σ 2 ω + f0 2 2 ω p = f 2 0 p (V ψ (ζ + β 0 y)) 2 ) (V ψ Φ p (3.3.79)., (quasi-geostrophic omega equation). 3.3.2, 10 5 s 1 ( 10 ),, R o 1, L/a 0.1, ε 10 2, βl/f 1 (3.3.80)., ε (3.3.49) R i = 100.,, L f, β f/l., (3.3.43) R 1 R o 1, (3.3.46) R 1 R o ε ε., R 1 = ε (3.3.81). (3.3.43) V 2 /10L 2,., (3.3.44) + V ψ (ζ + f) = 0 (3.3.82) (V ψ V ψ ) + 2 Φ fζ k f V ψ = 0 (3.3.83). (balance equation),. (3.3.82),.,, (3.3.46) fv 2., (3.3.81), (3.3.82)., (3.3.46).
78,.,., ( 4 ) 3.3.3, L/a 1, R o 0.01, ε 100, βa/f 1., (3.3.43) R 1 1 (3.3.84)., (3.3.46)., (3.3.43) (3.3.44), (V ψ + V χ ) f + fd = 0 (3.3.85) 2 Φ fζ k f (V ψ + V χ ) = 0 (3.3.86).,., V = V ψ + V χ = f 1 k Φ (3.3.87),., (3.3.45), (3.3.46), (3.3.87)., V ( ) ( 4 ).,.,,., ( 7 ).
79 3.4,.,. Charney(1962), R o (balance system).,. + (V ψ + V χ ) (ζ + f) + ω p +(f + ζ)d + k ω V ψ p = 0 (3.4.88) (V ψ V ψ ) + 2 Φ fζ k f V ψ = 0 (3.4.89) Φ p + (V ψ + V χ ) Φ p. V ψ = k ψ, + ω p p V χ = χ [ p Φ p κφ ] = 0 (3.4.90) (3.4.91) ζ = 2 ψ, D = 2 χ (3.4.92).,.,. ψ Φ, (balance equation).,.,,.,.,., Ro 2.,., k f V ψ.,., (3.4.89),., f *6. f,. *6 f, f f 0.
80,.,.,.,.,,.,.