Numerical evaluation of tsunami wave hazards in harbors along the south china sea
This presentation is the property of its rightful owner.
Sponsored Links
1 / 32

Numerical Evaluation of Tsunami Wave Hazards in Harbors along the South China Sea PowerPoint PPT Presentation


  • 74 Views
  • Uploaded on
  • Presentation posted in: General

Numerical Evaluation of Tsunami Wave Hazards in Harbors along the South China Sea. Huimin H. Jing 1 , Huai Zhang 1 , David A. Yuen 1, 2, 3 and Yaolin Shi 1 1 Laboratory of Computational Geodynamics, Graduate University of Chinese Academy of Sciences

Download Presentation

Numerical Evaluation of Tsunami Wave Hazards in Harbors along the South China Sea

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Numerical Evaluation of Tsunami Wave Hazards in Harbors along the South China Sea

Huimin H. Jing 1, Huai Zhang1, David A. Yuen1, 2, 3 and Yaolin Shi 1

1Laboratory of Computational Geodynamics,

Graduate University of Chinese Academy of Sciences

2Department of Geology and Geophysics, University of Minnesota

3Minnesota Supercomputing Institute, University of Minnesota


Contents

Contents

1. Introduction

2. Numerical experiments

2.1 Governing equations

2.2 Finite difference scheme

2.3 Numerical Model

3. Results and conclusions


1 introduction

1. Introduction

The probability of tsunami hazards in South China Sea.

The Manila Trench bordered the South China Sea and the adjacent Philippine Sea palate is an excellent candidate for tsunami earthquakes to occur.

The coastal height along the South China Sea is generally low making it extremely vulnerable to incoming waves with a height of only a couple meters.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Historical earthquakes in South China Sea and its adjacent regions


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

The results of the probabilistic forecast of tsunami hazard show the region where the wave height is higher than 2.0m and between 1.0-2.0m with a grid resolution of around 3.8km (Y. Liu et al. 2007).

In order to investigate the wave hazard in the harbors, simulations in higher precise are needed……


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

2. Numerical experiments

Shallow water equations

Conventional Boussinesq equations

Weakly Dispersive

Non dispersive

Dispersive

Deep water wave

Shallow water wave

L < 2h

L > 20h

Extended Boussinesq equations


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

2.1 Governing equation

z,w

Ω

L

y,v

h(x,y,t)

D

hB(x,y)

x, u

is the basic parameter in the theory of shallow water model:


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Derivation of the Shallow Water Equation


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Derivation of the Shallow Water Equation

For mass conservation equation


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Derivation of the Shallow Water Equation

For mass conservation equation


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Derivation of the Shallow Water Equation

For momentum conservation equation


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Derivation of the Shallow Water Equation

For momentum conservation equation


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Governing equation


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

2.2 Finite difference scheme

  • We simplify the equation into a linearized form

  • In our program, leap-frog scheme of finite difference method has been used to solve the SWE numerically and to simulate the propagation of waves. The leap-frog algorithm is often used for the propagation of waves, where a low numerical damping is required with a relatively high accuracy.


Simplify the equation into a linearized form

Simplify the equation into a linearized form

  • Let H(x,y) be the still water depth, and (x,y,t) be the vertical displacement of water surface above the still water surface.

  • Then we get

  • It follows from the definition

    where C is a constant.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Simplify the equation into a linearized form

  • Taking the partial

    derivatives of h(x,y,t)

  • We linearized the equation by neglecting the product terms of water level and horizontal velocities to obtain the following linearized form of the SWE.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Staggered Leap-frog Scheme

  • The leap-frog scheme is used to solve the SWE numerically and to simulate the propagation of waves.

  • Staggered grids (where the mesh points are shifted with respect to each other by half an interval) are used.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Discretization of staggered leap-frog scheme


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

2.3 Numerical model

  • Model components

  • a. the actual topography bathymetry data

  • b. the wave propagation simulation packages

  • c. scenarios of the wave source

  • Considering that we haven’t the high precise actual bathymetry data of the harbors along South China Sea, we use the data of the Pohang New Harbor in the southeast part of South Korea instead.


Topography of pohang new harbor

Topography of Pohang New Harbor


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Comprised topography data

The data of the compute area is comprised by topography data on the land (SRTM3, with a grid resolution of around 90m ) and bathymetry data of the seabed (SRTM30, with a grid resolution of around 900m ) .

In our numerical model, the grid size of the computational area is about 50m while the time step is 0.05s.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Scenario for plane wave source

When the tsunami comes from far field, the incident waves near the harbor area can be approximately considered as plane waves.

Plane wave function is as following:

Supposed the wave height is about 1m in the far field ocean, and carried on our simulations on the actual bathymetry data with the wave propagation packages.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Animations of the different sources

The reflection, diffraction and interference phenomenon of the waves are illustrated by the animations.

Water surface elevation track recorder points

The time series data of the water level vary with time have been recorded.

3.Results and conclusions


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

The results of point source case (from the east)


The results of plane wave case from south direction

The results of plane wave case (from south direction)


The results of plane wave case from east direction

The results of plane wave case (from east direction)


The results of plane wave case from north direction

The results of plane wave case (from north direction)


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Water surface elevation track recorder


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Maximal wave height at the track recorder points

By doing comparisons in the cases with different incident waves at the same point we get the effects of wave direction.

By doing comparisons in the same incident wave case at different recorder points we get the effects of water depth.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

3. Conclusions

The numerical simulations can be conducted to evaluate the reasons of harbor hazards and investigate the effects of different incident waves.

The direction of incident waves affect the wave hazard in a harbor.

The wave height in the coast area would be 7-8 times higher than it is in the ocean.

Water depth is the significant factor which affects the wave height.


References

References:

Fukao, Y., Tsunami earthquakes and subduction processes near deep-sea trenches, J. Geophys. Res., 1979, 84, 2303-2314.

Liu, Y., Santos, A., Wang, S.M., Shi, Y., Liu, H. and D.A. Yuen, Tsunami hazards along the Chinese coast from potential earthquakes in South China Sea, Phys. Earth Planet. Inter., 2007, 163: 233-244.

YEE, H.C., WARMING, R.F., and HARTEN, A.,Implicit total variation diminishing (TVD) schemes for steady-state calculations, Comp. Fluid Dyn. Conf. 1983, 6, 110–127.

ADAMS, M.F. (2000), Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics, Numerical Linear Algebra with Applications 11(2–3), 141–153.

BREZINA, M., FALGOUT, R., MACLACHLAN, S., MANTEUFFEL, T., MCCORMICK, S., RUGE, J. (2004), Adaptive smoothed aggregation, SIAM J. Sci. Comp. 25, 1896–1920.

WEI, Y., MAO, X.Z., and CHEUNG, K.F., Well-balanced finite-volume model for long-wave run-up, J. Waterway, Port, Coastal and Ocean Engin. 2006, 132(2), 114–124.

P. Marchesiello, J.C. McWilliams and A. Shchepetkin, Open boundary conditions for long term integration of regional oceanic models, Ocean Modell. 2001, 3, pp. 1–20.

E.D. Palma and R.P. Matano, On the implementation of passive open boundary conditions for a general circulation model: the barotropic mode, J. Geophys. Res 1998, 103, pp. 1319–1341.

Huai Zhang, Yaolin Shi, David A. Yuen, Zhenzhen Yan, Xiaoru Yuan and Chaofan Zhang, Modeling and Visualization of Tsunamis, Pure and Applied Geophysics, 2008, 165, pp. 475-496.


Numerical evaluation of tsunami wave hazards in harbors along the south china sea

Thank you for your attention!


  • Login