Some features of the landslide mechanism of the surface waves generation in real basins
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Some features of the landslide mechanism Some features of the landslide mechanism of the surface waves generation in real basinsof the surface waves generation in real basins
Institute of computational technologies SB RAS
Novosibirsk, Russia
Beisel S., Chubarov L., Khudyakova V., Shokin Yu.
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Novosibirsk, Tsunami-2009
Previous studies:•very simple bathymetry: linear slope + flat bottom,•Watts’s law of motion.
Questions:•Nonlinearity, dispersion – when and where?•Which NLD model is better?
Methodology:•Numerical modelling (SWE, Full model for potential flow)•Laboratory experiments
Shokin Yu.I., Fedotova Z.I., Khakimzyanov G.S., Chubarov L.B., Beisel S.A. Modelling surfaces waves generated by a moving landslide with allowance for vertical flow structure// Rus. J. Numer. Anal. Math. Modelling. – 2007. – Vol. 22. – №1. – pp. 63–85.
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Novosibirsk, Tsunami-2009
Now:From model bathymetry to «real» one
• The «reality» during the wave propagation• The «reality» in the law of landslide motion
From 1D simulation to 2D simulation • 2D effects in the law of landslide motion• 2D effects during the wave propagation
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Novosibirsk, Tsunami-2009
Area of interest:Mediterranean Sea, Israeli coast
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Novosibirsk, Tsunami-2009
( ) ( , )bt slz h x h x t ( )btz h x – bottom
( , )slz h x t – landslide
0 0( , ) ( ( ))sl slh x t h x x x t
0 0
2 21 tanh ( ( ) / 4) 1 tanh ( ( ) / 4)
cos cos( , )1 tanh / 4 1 tanh / 4[ ( )][ ( )]
[ )][ )]( (c c
sl
x x t L x x t Lx t
L Lh h
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Novosibirsk, Tsunami-2009
2
2sl a g b d
d sV F F F Fdt
Slide:
2 ( 1)sin ,t
d
gVu
C TW
0
1sin ,
m
a gC
00
( ) ln cosh ,t
s t st
,
0
2
0 a
us t 0
0
,tu
ta
const
New, 2009:
Watts, 1998:
( ) 22
0 02( )
1( ) ( ) ( ( ))sin ( )
2
r
l
x t
sl w w sl w sl d w
x t
d S dSC V Wg h x x x t x dx C TW
dt dt
22
2
1( ) ( ) sin
2sl w w sl w d w
d S dSC V Vg C TW
dt dt
( ) tan ,bth x x
V – volume,W – width,T – thickness,L – length,
sl – landslide density,
w – water density,
sl
w
– specific density,
wC – added mass coefficient,
– drag coefficientdC
aF – added mass force, gF – gravitational force,
bF – buoyancy force, dF – fluid dynamic drag force,
( )x
Laws of motion
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2.1 Approximation of Watts’ law for linear slope:
3. Approximation of Watts’ law for real slope “real” in motion law:
1. Watts’ law for linear slope
2.2 Approximation of Watts’ law for real slopeconstant in motion law:
2
0( )2
ts t a ( )tu u
( ) ts t u t ( )c stopx x
02 , ta const u const
( ) ( ) ( ) ( )i i
c sl i i sl ix x
x h x x h x 0 0 ( ( )),ca a x ( ( )),t t cu u x
Different laws
0
1.0,
1.5,
17900.0,
39500.0
( 0.5 ),
5000.0,
25
stop
d w
stop
x
C C
x
x
L
T
4. New law for real slope
+
+
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Different laws. Free surfaces
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Novosibirsk, Tsunami-2009
Different laws. Mareograms
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Novosibirsk, Tsunami-2009
( )
1 0 0
( )
( ( )) sin ( ) cos ( )r
l
x t
sl f
x t
I h x x x t x C x dx
22
1 22
1( ) ( ) ( )
2sl w w sl w sl w d w
d S dSC V WgI W I C T
dt dt
New law with friction
( )
2 0 0
( )
( ( )) ( )r
l
x t
f sl
x t
I C h x x x t K x dx 3
2'' '( ) ( ) 1 ( )bt btK x h x h x
– bottom curvature
*tanfC
* – friction angle
2
2sl a g b d n
d sV F F F F Fdt
nF – dynamic friction force
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Different friction angles
Linear slope: Real slope:
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Linear slope: Real slope:
Different friction angles. Mareograms
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Different submergences
Linear slope: Real slope:
* 2
* 1
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Different submergences. MareogramsLinear slope: Real slope:
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Novosibirsk, Tsunami-2009
0 20000 40000 60000 80000
X, м
-1600
-1200
-800
-400
0
Гл
уби
на,
м
0
2
4
6
8
Уго
л н
акл
он
а, г
ра
дус
ы
3D reliefs
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Novosibirsk, Tsunami-2009
Free surfaces
tt = 40 = 40 secsec tt = 120 = 120 secsec tt = 300 = 300 secsec
tt = 500 = 500 secsec tt = 860 = 860 secsec tt = 1000 = 1000 secsec
t_stopt_stop = = 850850 secsec
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Novosibirsk, Tsunami-2009
Free surfaces: 1D vs 2D
- 1D - 2D
tt = 40 = 40 secsec
0 20000 40000 60000 80000
X, м
-4
0
4
Ам
плит
уда,
м
tt = 120 = 120 secsec
0 20000 40000 60000 80000
X, м
-4
0
4
Ам
плит
уда,
м
tt = 300 = 300 secsec
0 20000 40000 60000 80000
X, м
-4
0
4
Ам
плит
уда,
м
tt = 500 = 500 secsec
0 20000 40000 60000 80000
X, м
-4
0
4
Ам
плит
уда,
м
tt = 860 = 860 secsec
0 20000 40000 60000 80000
X, м
-4
0
4
Ам
плит
уда,
м
tt = 1000 = 1000 secsec
0 20000 40000 60000 80000
X, м
-4
0
4
Ам
плит
уда,
м
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Thank you!