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8/18/2019 Capitulo3.Descripción modeloSWAH
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8/18/2019 Capitulo3.Descripción modeloSWAH
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8/18/2019 Capitulo3.Descripción modeloSWAH
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∂η
∂t +
∂ (h + η)u
∂x = 0
∂u
∂t + u
∂u
∂x + g
∂η
∂x +
1
h + η
ηˆ
−h
∂q
∂xdz + cf
u |u|
h + η =
1
h + η
∂ (h + η)τ xx
∂x
t
x
z
u
x
η h
q g
cf τ xx
η
ˆ −h
∂q
∂x
dz = 1
2
(h + η)∂q b
∂x
+ 1
2
q b∂ (η − h)
∂x
q b q b
q |z=η − q |z=−hh + η
= − q b
h + η =
1
2
∂q
∂z
z=η
+ 1
2
∂q
∂z
z=−h
ωs ωb z
∂ωs
∂t =
2q bh −
∂ωb
∂t
ωb = −u∂h
∂x
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∂u
∂x +
ωs − ωbh + η
= 0
ν t(x,y,t)
τ xx = 2ν t∂u
∂x
ν t
∂η
∂t +
∂ (h + η)u
∂x = 0
∂u
∂t + u
∂u
∂x + g
∂η
∂x +
1
2
∂q b
∂x +
1
2
q b
h
∂ (η − h)
∂x + cf
u |u|
h + η =
1
h + η
∂
∂x
(h + η)ν t
∂u
∂x2
ωb = −u∂h
∂x
∂ωs
∂t =
2q bh −
∂ωb
∂t
∂u∂x
+ ωs − ωbh + η
= 0
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|u|t
x ≤ 1.
xi+1/2
xi+1/2 = ix, i = 0,...I
x xi = (xi−1/2 + xi+1/2)/2 u i + 1/2,
η, h, q b, ν t, wb
ws
(n +1/2)t t n tn = nt,
un+1/2i+1/2 − u
n−1/2i+1/2
t + u
n−1/2
i+1/2 (Lxu)
n−1/2
i+1/2 + g
ηni+1 − ηni
x +
q n+1b,i+1 − q n+1b,i
2x +
q Xb,i+1/2
n+1hX
i+1/2
nηni+1 − η
ni − hi+1 + hi
2x + cf
un+1/2i+1/2
un−1/2i+1/2hX
i+1/2
n =
ν t,i+1hni+1
un−1/2i+3/2 − u
n−1/2i+1/2
− ν t,ih
ni
un−1/2i+1/2 − u
n−1/2i−1/2
hX
i+1/2
nx2
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ηn+1i − ηni
t +
ĥni+1/2un+1/2i+1/2 − ĥ
ni−1/2u
n+1/2i−1/2
x = 0
Lx
a
ĥi+1/2
ĥi+1/2 =
ηi + min(di, di+1), if ui+1/2 > 0ηi+1 + min(di, di+1), if ui+1/2 < 0
max(η, ηi+1) + min(di, di+1), if ui+1/2 = 0
t ≤
x2
2ν t
ν t = min
ν t,x2
2t
.
ub =
g
h + η (2ηb − η)
ub ηb
∂u
∂t +
gh∂u
∂x = 0
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∂η
∂t > α
gh
α
α
n
cf = n2g
h1/3
cf =
κ
ln (h/z 0)− 1
2
κ = 0.4 z 0 = ks/30
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kh ≤ 3
kh =
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