KENZOU

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1 KENZOU A ============================

2 4 v = v t + (v v = K p (4. A ( B = ( BA (A B (v v = ( v v v rot v ( v x ( v v = v x x, v v y y y, v v z z = z 2... (v v = 2 q2 v rot v ( vx 2 x, v2 y y, v2 z = z 2 q2 (q = v v t = K p 2 q2 + v ω, ( ω = rot v (4.2 p P dp = dp P = p dp (4.3 P = p ( v (P t = K + 2 q2 + v ω ( φ v v = φ ( φ K = t + 2 q2 + P (4.6 K K U K = U 4.2 ( φ t + 2 q2 + P + U = 0 (4.7 ( φ φ 4.7 x, φ y, φ = 0 z φ t 4.7 t f(t φ t + 2 q2 + P + U = f(t (

3 4.2 v/ t=0 K = U 4.5 ( 2 q2 + P + U = v ω (4.9 H = 2 q2 + P + U (4.0 ω = 0ω / v v ω = 0 H = const H = const P = p/ U = gz p + 2 q2 + gz = const (4. const const -7 20m/sec m F ig.5 v P z v 2 P 2 z 2 P + 2 v2 + gz = P v gz 2... z 2 z = 2g (v2 v2 2 + P P 2 g P = P 2 v 2 = 0 v = 20 z 2 z = 20.4m -8 Q q θ Fig.6 Q 2 Q 3 F ig.6 Q 2 q 2 Q θ P P 2 θ q F P 3 y x q 3 Q 3 3

4 x, y Fig.6 Q = Q 2 + Q 3 (4.2 p + 2 q 2 = p + 2 q 2 2 = p + 2 q q = q 2 = q 3 (4.3 x Q q cos θ Q 2 q 2, Q 3 q 3 Q q cos θ = Q 2 q 2 Q 3 q 3 ( Q 2 Q 3 = Q cos θ ( Q 2 Q 3 Q 2 = ( + cos θq /2, Q 3 = ( cos θq /2 F F = P (P 2 cos θ P sin θ P = Q q, P 2 = ( + cos θq q 2 /2, P 3 = ( cos θq q 3 /2 F = Q q {( + cos θq 2 /2 ( cos θq 3 /2} Q cos θ = Q q sin 2 θ P p = k γ k (4.6 kγ γ P = dp = γ p γ (4.7 p = 0 P = 0 U = 0 2 q2 + γ γ c 2 q2 + P = const (4.8 p = γ 2 c = const, (4.9 c 2 = γ P (4.20 q = q2 + γ c2 = γ c2 0 (4.2 4

5 c 2 c 2 0 = q2 2 qm 2, q m = γ c 0 (4.22 q q m q m p c 2/(γ, p γ c 2γ/(γ 4.22 = ( q2 γ 0 qm 2 p = ( γ q2 γ p 0 qm 2 (4.23 ( γ } p q = q m { 2 γ p 0 (4.24 p 0 p q Fig.7 v q s φ φ = q(s, φ = q(s (4.25 s 4.3. q = Q Q t t 4.25 φ = q(ts φ t + 2 q2 + p ( + gz = f(t s + dt 2 q2 + p + gz = f(t (4.26 y F ig.7 2 F ig.8 p 2 q p 0 p z 2 z s x h l 2 p q 5

6 Fig.7 p z qs + 2 q2 + p + gz = qs + 2 q2 + p + gz (4.27 p p = g(z z q(s s ( q q 2 p q = s 2 s { } (p 2 p + g(z 2 z ( Fig.8 l 2 z = z 2 = 0 p 2 = p s 2 s = l 4.29 q = l (p p (4.30 p p p + gh = p + 2 q2 (4.3 q = 2l ( q2 q 2, ( q = 2gh (4.32 q 0 dq q 2 q 2 = t... q = q tanh t 2T, 0 2l dt ( q tanh = t q q 2l ( T = l/q q q p 4.3 ( p = p + gh tanh 2 t = p + gh sech 2 t 2T 2T t = 0 p + gh p Fig.9 q = 0p = 0l =, h = (4.33 F ig.9 qp q q = 0 tanh 5t p = 9.8sech 2 5t t 6

7 4.3.2 s q(s, t(s = Q(t q s t q = Q(t (s 4.25 φ = q = Q(t (s (4.34 ( φ + 2 Q2 2 + p + gz = f(t (4.36 p p = g(z z Q s2 ( 2 Q2 2 2 Q s (4.37 s2 Q s + ( 2 Q p 2 p + g(z 2 z = 0 ( l p 2 = p = p, z 2 z = h 2 = Q s2 s + 2 Q2 0 2 gh = 0 (4.39 s s2 s Q Q = 0 q l 0 0 = l 0 l q + 2 q2 gh = 0 q = 2l (q2 q 2 (q = 2gh ( s = R / K v = (v v = p (4.4 F ig.20 R n R n s t 7

8 Fig.20 st q v = qt f s = t f = t t s s ( v v = q s q t (qt = q t + q2 s s nr κ t s = R n, 4.4 κ = R (4.42 p = q 2 2 s t q2 κn (4.43 p s t n p s = q 2 2 s, p n = κq2 ( P p s = s ( p dp p ( p dp s + 2 q2 = 0 P + 2 q2 = const (4.45 s ω 2 Ω K = U p 4.5 v (P t = + U + 2 q2 + v ω rot rot(dv/dt = ω/ trot = 0 ω t = rot(v ω (4.46 rotv ω = v( ω ω( v + (ω v (v ω 2 (3.6 = t + v 2 (3.3 v = 8

9 4.46 rot(v ω = ω t... = v( ω ω( v + (ω v (v ω = ω + (ω v (v ω = ω (v ω... ω = ω ( ω = ω + (v ω t + (ω v ( ( ω = ω ω 2 ( ( ω ω = v ( t = 0 ω = [ ( ] {( } ω ω = v = 0 (4.49 t=0 t=0 t ( ω = t= t ( [ ω + t=0 ( ] ω t = 0 (4.50 t=0 ω = 0 t = 0 ω 0 ω = 0 t = 0 ω = Γ( = v dr = v s = (udx + vdy + wdz = ( φ φ φ dx + dy + x y z dz = dφ (4.5 circulationγ( v s v φ 2 rotv = ω Γ( = v dr = (rotv n d (4.52 Γ( = ω n d = ωd (4.53 Γ( = 0 2 2! div! =! = rotv = 0 9

10 Fig.2- Γ Γ ( AB A B ( B A Γ ( F ig.2 F ig.2 2 A B A Γ Γ Γ A Γ Γ ( = 0 Γ ( = + AB + + = Γ + + = Γ ( Γ( = 0 BA AB AB... Γ ( = Γ( ( A ΓA Γ Fig.2-2 AA A AA ω n d ω n = 0 + = Γ( + Γ( = 0 AA + A A + A A AA... Γ( = Γ( ( ω n σ Γ( = ω n d = ω d = ωσ (4.56 Γ( ω Γ( = ω n d = ωσ (

11 Γ( t = 0 0 t Γ( F ig.22 t = 0 0 t = t 4 Γ( = v dr = (v dr c v (v dr = dr + v dr (4.58 K v dp = (U + P, K = U, P = 2 r r 2 dr = r 2 r (4.59 dr = (r 2 r = v 2 v = dv (4.60 ( (v dr = (U + P dr + v dv = d(u + P + d ] Γ( = [ 2 q2 U P 2 v2 ( = d 2 q2 U P (4.6 q P U Γ( = const = Γ( 0 (

12 ( A r r = r(t = (x(t, y(t, z(t (A. t a t b s s [t 0, t] P Q[ t, t + t ] P Q ( x P Q = 2 ( 2 ( 2 y z ( x 2 + ( y 2 + ( z 2 = + + t t t t (dx.. 2 ( 2 ( 2 dy dz. = lim P Q = + + dt (A.2 t 0 dt dt dt.. s t (dx 2 ( 2 ( 2 dy dz t. s = = + + dt = dr s 0 dt dt dt dt dt (A.3 t 0 t s s t 0 r = r(s (A.4 2

13 F ig.a dr dt F ig.a 2 φ dφ = u φ u = P r(s r Q r(s + s P θ u dφ O s s r rs + s Q r = P Q r s s 0 t s t = dr t Q P θ κ = dθ = lim θ s 0 s κ = /κ (A.5 (A.6 φ(x, y, z P u P u P s r(s P φ u φ(r(s u φ(p + su φ(p = lim = dφ s 0 s = φ x x s + φ y y s + φ z z s = u φ φ(x, y, z n φ dφ/dn (A.7 φ = dφ n (A.8 v dr = (rotv nd (A.9 F ig.a 3 n v dr 3

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2 2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6

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