7 * River Configuraion in Middle-Lower Reach of River Bain Hirohi TAKEBAYASHI, Facul of Engineering, Univeri of Tokuhima 1 1 (a (b 1 4 3 1 *770-8506 -1 E-mail: akeh@ce.okuhima-u.ac.jp
5 3 6 km 7 km 8.1 9 9 3 8
Ug =ξ ug +ξ vg, Vg =η ug +η vg (5 u g v g Λ. 9 z z b Λ = 1z z b Λ = λ z b λ 8 10 J = 1 (1 ξ η η ξ hu hu hu + ( ξ + U + ( η + V ξ = J η, η = J ξ, ξ = J η, η = J ξ ( J ξ J η J hu ξ ξ ξ + ( ξ + U + ( η + V J ξ η ξη hv ξ ξ ξ + ( ξ + U + ( η + V J ξ η ξ +ξ z ξη +ξη z = gh + ξ = ξ 10 J J ξ η (6 τbξ Fvξ ξ ξη + ( hσ + ( hσ ρj ρj J ξ J η ξη ξξ + ( hτ + ( hτ J η J ξ ξη ξξ + ( hτ + ( hτ J η J ξ ξ 1 + ( hσ + ξη ( hσ J ξ J η 11 hv hv hv z h h + ( ξ + U + ( η + V Λ + ( ξ + U + ( η + V J ξ J η J J ξ J η J (3 hu η η η hg hg + ( ξ + U + ( η + V + ( ξ + Ug + ( η + Vg = 0 J ξ η ξ J η J hv η η η + ( ξ + U + ( η + V z J ξ η (7 h, h g U V ξ ξη +ξη z η +η z = gh + η J J ξ η τbη Fvη ηξ η + U =ξ u+ξ v, V =η u+η v (4 ( hσ + ( hσ ρj ρj J ξ J η u v ηξ ηη + ( hτ + ( hτ U g V g ξη J ξ J η
30 8 ηξ ηη + ( hτ + ( hτ J ξ J η u v σ = ν k, σ = ν k (17 3 3 ηξ η + ( hσ + ( hσ J ξ J η v u τ =τ =ν + (18 g ρ τ bξ τ bη ξη ν= ( κ 6 uh * (19 k =.07u* (0 τ bξ =ξτ b +ξτ b, τ bη =ητ b +ητ b (8 ν κ k τ τ 15 ub vb τ =τb, τ =τb (9 ub + vb ub + vb τ b =ρu * (10 16 F vξ F vη ξη ng m u + v u* = 1 3 ( u + v or u* = (11 R ( 6+.5ln( hk F u * n m =ξ v F +ξ v F, ξ v Fvη =η Fv +η Fv (1 R k F v F v (11 u v F v = Fv, F v = Fv ( u + v u + v u b v b Fv 1 = Cdvλ v ( u + v h (3 ρ C dv 1.0 ub = ubcoα vbin α (1 λ v (3 vb = ubin α + vbcoα (13 ub = 8.5u* (14 h 17 vb = N* ub (15 r Darc α = arcan ( vu, N * 1 7.0 13 zb zb ug = kg ξ +η (4 r ξ η 14 zb zb v u v u vg = kg ξ +η (5 u u v + v u v ξ η 1 = (16 r ( u + v 3 k g k g σ σ τ τ
18 f bk c b E b 19 E d1 1 f d1k 1-λ 4 4 交換層と第 1 堆積層 Ebe 1 = τ の粒径階ごとの質量保存則は, 以下のようである 0 co ( an an * m (8 dm cb θ φ θ ce b bfbk zb + ( 1 λ Fbk J J ce q b bf bk bk ξ ce q b bf bk bηk + ξ + + η + ξ J J J J η 1 + wk( cbek cbk = 0 J E f E = J J d1 d1k d1 Fdk 0 F, 0 bk = fd1 k zb Fbk = fbk, zb 0 (6 31 ここで,d m φ τ *m 交換層厚さ E b は, 河床に十分土砂が存在し, 且つ, 全粒径の土砂が移動する条件では, 平衡交換層厚さと等しくなるが, 粗粒分などが限界掃流力以下の時は, 平衡交換層厚さよりも薄くなる. q bξk q bηk ξη k qbξ k =ξ qbk +ξ qbk, qbη k =η qbk +η qbk (9 q bk q k 19, 1, 4, 0 Fdk = fd1 k zb (7 qbk = qbk coβ k Fdk = fbk, zb 0, qbk = qbk inβ k (30 3 17ρu * e u * ck u * ck E b 交換層厚さ,f bk qbk = 1 Kc 1 Kc fbk (31 ( ρ ρ g k f dmk m u* u* k, c b ρ u *e 上面に設定 するため, 土砂濃度 c b は静止堆積濃度 が想定され, 河床の空隙率 1-λが用いられる. さらに, 交換層厚さ E b は, 交換層内の土砂の 90% 粒径程度 の値が用いられている 1. また, 取り扱う現象のスケ ールによっては, 砂河床に対して砂堆の波高を交換 19 層厚 E b として用いられる. つまり, 交換層上面を 河床面と考えた場合, 交換層厚さの物理的意味は u + v 薄れ, 粒度を適切に予測できるように無理のない値 u* e = (3 h を交換層厚さと考えて用いられているようである. 一 6+.5ln dm( 1 * m + τ 方, 河床面を交換層下面に設定した場合, 交換層は掃流砂層となり, c b u *ck k 平衡交換層厚さ E be は, Egahira and Ahida 3 19, 5 bk
3 log1019 d 8 k u* ck = u* cm dk dm 0.4 (33 log10 ( 19dk dm d 36ν 36ν m wfk = + gd 3 3 k (43 3 gdk gd u* ck = 0.85u* cm dk dm 0.4 (34 k k 6 c bek 9 0.05 Lane and Kaline 30 1.61 1 u w * fk cbek = 5.55 ep fbk ( :ppm(44 wfk u * 7 1, 4 K c 5% 9 ρ + 1coαan θ + in αan θ ρ ρ Kc = 1+ (35 µ k c θ θ k c bk 31 zb z b θ = arcan ξ +η (36 c ( w bk ξ η c = ( 1 e β fkh, β = (45 β D zb z b D θ = arcan ξ +η (37 h ξ η µ k α α= arcan( v b u b (38 hc k J β k hc hc + ( ξ + U + ( η + V ξ J η J in α ΠΘ( u* ck u* an θ anβ k = (39 1 coα ΠΘ( u* ck u* an θ = w fk ( cbek cbk J Π= K ld + 1 µ (40 Dξ + Dξ c (46 + h ξ J Θ = 1 ( 1+ an θ + an θ (41 ξ D ξη + Dξη c Θ =Θ +ρ ( ρ ρ co θ (4 + h ξ J η K ld (0.85 Dξη + Dξη c w fk Rube + h η J ξ h
33 (m 6000 5000 4000 3000 (m 000-3000 -1000 1000 3000 5000 7000 9000 11000 13000 5 33 Dη + Dη c 7000 + h η J η 6000 5000 D D 4000 3000 000 1000 6 0 0 5 10 15 0 5 30 (hr ce b b zb + ( 1 λ 6 J J 9.5 n q n ξce b b bk ξ η q ce b b bηk + + + + J k= 1 J (47 Cae 1 ξ η J k= 1 J 9 n Cae 1 + wk ( cbek cbk = 0 8.5 k = 1 J 8 n 7.5 7 6.5 3 (m 3 / (m 6 3 5.5 0 1000 000 3000 4000 5000 6000 7000 3.1 (m 3 / 7-5 7 31 49km 1999 7 8km.1km 1999
34 (m 5000 4800 10m/ 4600 4400 400 4000 (m 500 1500 500 3500 4500 5500 6500 (m 0h (56 m3/ 5000 4800 10m/ 4600 4400 400 4000 (m 500 1500 500 3500 4500 5500 6500 14h (6011 m3/ (m 5000 Cae1 4800 10m/ 4600 4400 400 4000 (m 500 1500 500 3500 4500 5500 6500 14h (6011 m3/ Cae 8 49km 49km 9.8km 15.6km 001 3. 7 Cae 1 Cae - 9.8km 15.6km 3cm 10 49mm Cae 1-6 1999 9 17 8 49km Cae 1 Cae (31 Cae 1 Cae 1 Cae Cae Cae 1 1999 9 Cae 1 Cae
35 10 0.45 植生域 基準点からの高さ (m 8 6 4 0 Cae 1 ( Cae ( 0.4 0.35 0.3 0.5 0. - -4-6 Cae 1 ( Cae ( -8 0 0 50 100 150 00 50 300 350 400 左岸からの距離 (m 9 8.km 30 8.km Cae Cae 1 Cae 1 160m 1 Ohmori, H.: Eroion rae and heir relaion o Cae vegeaion from viewpoin of world-wide diribuion, Bullein of he Deparmen of Geograph, Univeri of Toko, 15 (1983 4 77-91,. 8 (1997 3 Blue Back (1994. 4 5 :, Vol. 677 No.II-55 (001 75-86. 6 Okabe, T. and Takebaahi, H.: Numerical eimaion of counermeaure again edimenaion in Maaki Dam Reervoir, Japan, Environmenal Hdraulic and Suainable Waer Managemen, Lee & Lam 0.15 0.1 0.05 河床材料の平均粒径 (m
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