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TSUNAMI MODELING METHODS TO UNDERSTAND GENERATION AND PROPAGATION. HL. h. Parameters for wave motion Height H = 2a Length L Local water depth h Duration/period T Gravity g. Shoaling - PowerPoint PPT Presentation
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TSUNAMI MODELING TSUNAMI MODELING METHODS TO METHODS TO UNDERSTAND UNDERSTAND
GENERATION AND GENERATION AND PROPAGATIONPROPAGATION
Parameters for wave motion
Height H = 2aLength L Local water depth h Duration/period TGravity g
HL
h
Shoaling
Typical change in water depth as tsunamis leave the ocean for coastal waters is from around 4km
to 100m on the continental shelf to zero at the coastline.
The topography of this change is very relevant:for a steep approach there is much wave reflection and amplitudes are not greatly increased
consider ordinary waves at a cliff: 2
gently sloping topography, leads to large amplificationif 2D, then until a ~ h 4/1 ha
Approaching the shoreline
As they approach the shoreline ordinary wind generated waves break. Long waves such as tsunamis are more like tides, which only break in the special circumstances of long travel distances in shallow water. Then tsunamis are similar to tidal bores.
For example tsunamis can have periods approaching one hour, and in the River Severn near Gloucester spring tides can rise from low to high tide in one hour. The character of a bore depends strongly on the ratio
Rise in height of the waterdepth in front of the bore
= Hh
A bore may be undular, turbulent of breaking-undulardepending on the value of this ratio.
TSUNAMI MODELS
• TUNAMI N2• MOST• FUNWAVE• MIKE 21• DELFT 3D• AVI-NAMI• NAMI-DANCE• TELEMAC• …
HISTORY OF TSUNAMI MODELLING
• The TUNAMI code consists of;• TUNAMI-N1 (Tohoku University’s Numerical Analysis
Model for Investigation of Near-field Tsunamis, No.1) (linear theory with constant grids),
• TUNAMI-N2 (linear theory in deep sea, shallow-water theory in shallow sea and runup on land with constant grids),
• TUNAMI-N3 (linear theory with varying grids), • TUNAMI-F1 (linear theory for propagation in the
ocean in the spherical co-ordinates) and• TUNAMI-F2 (linear theory for propagation in the
ocean and coastal waters).
TSUNAMI MODELING
• Nonlinear Shallow Water Equations (NSW),• numerical solution procedure is from Shuto, N.,
Goto, C., Imamura, F., 1990 and Goto, C. and Ogawa, Y.,1991,
• TUNAMI N2 authored by Profs. Shuto and Imamura, and developed/distributed under the
support of UNESCO TIME Project in 1990s.
Governing Equations
0
y +hv
x+hu
t
0 x
y
u v
x
u
t
u
xgu
0y
y
vv
x
v
t
v
ygu
η : water elevationu, v : components of water velocities in x and y directionsy : bottom shear stress components ح ,xحt : timeh : basin depthg : gravitational acceleration
Non-linear longwave equations
uDhuM )(
,
vDhvN )(
0y
x
t
NM
0D D
MN
y
D
M
x
t
227/3
22
NMM
gn
xgD
M
0D D
N
y
D
MN
x
t
227/3
22
NMN
gn
ygD
N
M, N : Discharge fluxes in x&y directions
n : Manning’s roughness coefficient
Numerical Model “TUNAMI N1”
0
xg
t
u 0
yg
t
v
0][][
y
vh
x
uh
t
Mesh resolution and time step, grid size
Total reflection on land boundaries
Boundary Conditions
Reflection:
0n
ght
0n
Open Boundary:
Initial Condition: u(x,y,0)
v(x,y,0)
(x,y,0)
Numerical TechniqueFinite Difference " Leap Frog"
j+1
j
i
2
1
2
1,
k
jiN
21
21
,
k
jiN
2
1
,2
1
k
jiM 2
1
,2
1
k
jiM
1
,
k
ji
y
xi-1 i+1
j-1
y
x
k
ji
k
jitt ,
1
,
1
2
1
,2
12
1
,2
1
1 k
ji
k
jiMM
xxM
2
1
2
1,
2
1
2
1,
1 k
ji
k
jiNN
yyN
2
1
2
1,
2
1
2
1,
2
1
,2
12
1
,2
1,
1
,
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji NNyt
MMxt
Difference Scheme
Terms
0
xgD
tM
k
ji
k
ji
k
ji
k
ji
k
ji xt
gDMM ,,1,
2
12
1
,2
12
1
,2
1
k
ji
k
jiji
k
jiji
k
jihhD ,,1
,2
1,
2
1,
2
1,
2
1 21
k
ji
k
jiji
k
jiji
k
jihhD ,1,
2
1,
2
1,
2
1,
2
1, 2
1
k
ji
k
jiji
k
ji
k
ji
k
ji yt
hgDNN ,1,
2
1,
2
1,
2
1
2
1,
2
1
2
1,
Direction x
Direction y
h >
Convective Terms
2
1
,2
1
2
2
1
,2
1
31
2
1
,2
1
2
2
1
,2
1
21
2
1
,2
3
2
2
1
,2
3
11
21
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
D
M
D
M
D
M
xD
M
x
2
1
11,2
1
2
1
1,2
12
1
1,2
1
31
2
1
,2
1
2
1
,2
12
1
,2
1
21
2
1
1,2
1
2
1
1,2
12
1
1,2
1
11
1k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
D
NM
D
NM
D
NM
yDMN
y
Truncation in the order of x
2
1
2
1,1
2
1
2
1,1
2
1
2
1,1
32
2
1
2
1,
2
1
2
1,
2
1
2
1,
22
2
1
2
1,1
2
1
2
1,1
2
1
2
1,1
12
1k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
D
NM
D
NM
D
NM
xDMN
x
21
21
,
2
21
21
,
3221
21
,
2
21
21
,
2221
23
,
2
21
23
,
12
21
k
ji
k
ji
k
ji
k
ji
k
ji
k
ji
D
N
D
N
D
N
yD
N
y
Friction Term
2
2
1
,2
1
2
2
1
,2
12
1
,2
12
1
,2
13/7
2
1
,2
1
2
22
3/7
2
21
k
ji
k
ji
k
ji
k
jik
ji
NMMM
D
gNMM
D
g
2
2
1
2
1,
2
2
1
2
1,
2
1
2
1,
2
1
2
1,
3/7
2
1
2
1,
2
22
3/7
2
21
k
ji
k
ji
k
ji
k
jik
ji
NMNN
D
gNMN
D
g
Discretization
Tunami-N2
Programme TIME : Tsunami Inundation Model Exchange
RECENT TREND IN TSUNAMI MODELING
• Simulation and Animation
for Visualization
INPUT PARAMETERS
• Arbitrary shape bathymetry
• Tsunami source as initial condition
RECENT TREND IN TSUNAMI MODELING
• AVI-NAMI and NAMI DANCE simulation/animation software in C++ Language
• are brothers of TUNAMI N2
• authored by Pelinovsky, Kurkin, Zaytsev, Yalciner
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Wl Lmajor
Lminor
al al
ac
TERMS
• Bottom Friction
• Pressure
• Dispersion – FUNWAVE by Kirby
– Fujima
December 26, 2004
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
December 26, 2004
March 28, 2005
Andaman Source
1762
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
MACRAN FAULT
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Andaman Source
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Mindanao Source
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Hypothetical Tsunami Source at offshore Sabah as an example simulation in South China Sea
Pelinovsky, Kurkin, Zaytsev, Yalciner, Imamura
Hypothetical Tsunami Source at offshore Sabah as an example simulation in South China Sea
ASSESMENT OF TSUNAMI HAZARD
Simulation and animation of probable/credible tsunami scenarios, and understanding coastal amplification and arrival time of tsunamis
Acknowledgements Prof. Shuto, Imamura, Synolakis, Okal, Pelinovsky, Zaytsev
UNESCO IOC, Tohoku University Japan
Ministry of Marine Affairs and Fisheries Republic of Indonesia,
UTM, DID, ATSB, Dept. of Meteorolgy, Malaysia,
Middle East Technical University, METU, Yildiz Technical University, Chambers of Geological and Civil Engineers of Turkey,
Dr. Eng. Dinar Catur Istiyanto Ir. Widjo Kongko, M. Engand, Russian Colleagues and Team, American Colleagues and Team, Japanese Colleagues and Team, Prof. Ir. Widi
Agoes Pratikto, Dr. Ir. Subandono Dipsosaptono, Dr. Gegar Sapta Prasetya, Dr. Ir. Rahman Hidayat
THANKS and APPRECIATION THANKS and APPRECIATION
TUNAMI – N2
“Simulation” of propagation of long waves
solves for irregular basins
computes water surface fluctuations and velocities
is applied to Several Case Studies in Several Sea and Oceans
Linear Form of Shallow Water Equations in Spherical Coordinates
for Far Field Tsunami Modeling
Dispersion term is considered by Boussinesq Equation.
Long waves (small relative depth) avertical << agravitational
Velocity of water particles are vertically uniform.
0)cos(cos
1
NM
RtfN
R
gh
t
M
cos
fMR
gh
t
N
0
coscos
cos
1 2
1
2
1,
2
1
2
1,,
2
1,
2
12
1
,2
1
,
m
n
mjm
n
mj
n
mj
n
mj
m
n
mj
n
mj
NNMM
Rt
η : water elevationR : radius of earthM, N : discharge fluxes along λ and Өf : Coriolis coefficientg : gravitational acceleration
NfR
gh
t
MM n
mj
n
mj
m
mj
n
mj
n
mj
2
1
,2
1
,1,
2
1,
2
11
,2
1
cos
MfR
gh
t
NN n
mj
n
mj
m
mj
n
mj
n
mj
2
1
,2
1
1,,
2
1,
2
11
,2
1
sin
n
mj
n
mj
n
mj
n
mjNNNNN
2
1,
2
1,
2
1,1
2
1,14
1
n
mj
n
mj
n
mj
n
mjMMMMM
,2
11,
2
1,
2
1
2
1,
2
14
1
where;
2
1
2
1,
2
1
2
1,,
2
1,
2
112
1
,2
1
, coscosm
n
mjm
n
mj
n
mj
n
mj
n
mj
n
mj NNMMR
NRhRMMn
mj
n
mjmj
n
mj
n
mj
3
2
1
,2
1
,1,
2
12,
2
11
,2
1
MRhRNNn
mj
n
mjmj
n
mj
n
mj
5
2
1
,2
1
1,
2
1,
4
2
1,
1
2
1,
Computation Points for Water Level and Discharge
R1 = t / (Rcosm)
R2 = g.t / (Rcosm)
R3 = 2tsinm
R4 = gt / (R) R5 = 2tsinm+1/2
where; , , t : directions , , t : grid lengths : angular velocity
TWO-LAYER NUMERICAL MODEL FOR TSUNAMI GENERATION AND PROPAGATION
• The mathematical model TWOLAYER is used as a near-field tsunami modeling version with two-layer nature and combined source mechanism of landslide and fault motion
• In two-layer flow both layers interact and play a significant role in the establishment of control of the flow. The effect of the mixing or entrainment process at a front or an interface becomes important (Imamura and Imteaz, (1995)).
• Two-layer flows that occur due to an underwater landslide can be modeled using a non-horizontal bottom with a hydrostatic pressure distribution, uniform density distribution, uniform velocity distribution and negligible interfacial mixing in each layer (Watts, P., Imamura, F., Stephan. G., (2000)).
TWOLAYER
Theoretical Approach
• Conservation of mass and momentum can be integrated in each layer, with the kinetic and dynamic boundary conditions at the free surface and interface surface (Imamura and Imteaz 1995)).
η : surface elevation
h : still water depth
ρ : is the density of the fluid
1,2 : upper and lower layer respectively (Imamura and Imteaz,(1995))
• The numerical model TWO-LAYER is developed in Tohoku University, Disaster Control Research Center by Prof. Imamura.
• The model computes the generation and propagation of tsunami waves generated as the result of a combined mechanism of an earthquake and an accompanying underwater landslide.
• It computes the propagation of the wave by calculating the water surface elevations and water particle velocities throughout the domain, at every time step during the simulation.
• The staggered leap-frog scheme (Shuto, Goto, Imamura, (1990)) is used to solve the governing equations.
Numerical Approach
Numerical Approach
Points schematics of the staggered leap-frog scheme (Imamura, Imteaz (1995))
Test of the Model
• The model TWO-LAYER is tested by using a regular shaped basin for modeling of generation and propagation of water waves due to underwater mass failure mechanisms.
• In order to obtain accurate results the duration and domain of simulation as well as the characteristics of the mass failure mechanism must be chosen accurately and described very precisely. For stability the time step and grid size should also be selected properly.
• Rectangular basin w= 150 km. l= 125 km.
• Three boundaries of this basin (at East, North and West) are set as open boundaries to avoid wave reflection and unexpected amplification inside the basin as shown in the figure below.
• The land is located at the South
• Uniformly sloping bottom starting with -100m. elevation at land and deepen up to 2000 m with a slope of 1/60.
• Grid spacings: 400 m. with : 375 nodes in E-W : 313 nodes in S-N
• 22 stations were selected to observe the water surface fluctuations
Basin and Parameters
- solves the generation of the tsunami wave due to the mass failure mechanism at the source area
- calculates the water surface elevations at each grid point while propagating the wave in the basin.
- obtains the time histories of the water surface elevation at all grid points and stores 22 selected stations
TWOLAYER
Mass failure mechanism is generated at a smaller rectangular region inside the basin (w: 20 km.; l: 40 km )
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00
East-W est D irection (km .)
0.00
20.00
40.00
60.00
80.00
100.00
120.00
So
uth
-No
rth
Dir
ecti
on
(km
.)
1 2 3 4
5 6
h+ : increase of water depth in the eroded area due to the mass failureh- : decrease of water depth in the accreted area due to the mass failureL+ : length of the eroded areaL- : length of the accreted area
Initial and final profile of the sea bottom in the mass failure area
The conservation of the moved volume of sediment before and after the failure
h+ . L+ = h- .L-
Sea bottom
before mass failure
Sea bottom
after mass failure