Wave propagation through arrays of unevenly spaced vertical piles
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Wave propagation through arrays of unevenly spaced vertical piles Adviser ： Jeng-Tzong Chen Date: February 06, 2009 Place: HR2 307 Reporter : Yi-Jhou L in National Taiwan Ocean University Department of Harbor and River Engineering
description
Wave propagation through arrays of unevenly spaced vertical piles. Reporter : Yi-Jhou Lin. National Taiwan Ocean University Department of Harbor and River Engineering. Adviser ： Jeng-Tzong Chen. Date: February 06, 2009. Place: HR2 307. Outlines. Problem statement Numerical examples - PowerPoint PPT Presentation
Transcript of Wave propagation through arrays of unevenly spaced vertical piles
Wave propagation through arrays of unevenly spaced vertical piles
Adviser ： Jeng-Tzong ChenDate: February 06, 2009 Place: HR2 307
Reporter : Yi-Jhou Lin
National Taiwan Ocean UniversityDepartment of Harbor and River Engineering
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Outlines
Problem statement Numerical examples Concluding remarks
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Problem statement
.),,(,0);,,(2 Dzyxtzyx
})(),(Re{);,,( tiezfyxtzyx
kh
hzkigAzf
cosh
)(cosh)(
Governing equation:
Separation variable :
).,(,0 yxhzn
where
Seabed boundary conditions : inc
Original Problem
inc
Free-surface conditions :
, ( , , ).z t z x y yH H H z H x y t
2 2( ) ( , ) 0, ( , )k x y x y D
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Decompose two parts
inc
＝
Radiation field (typical BVP)
Free field
inc
Original Problem
inc inc
＋
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FlowchartOriginal problem
Decompose two parts
Free field Radiation field
Expansion
Fourier series of boundary densities
Degenerate kemelFor fundamental solution
Collocate of the real boundary
Linear algebraic system
Calculation of the unknown Fourier
BIE for the domain point
Superposing the solution of two parts
Total field
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Numerical examples
inc
Original Problem
inc
0.0
/ 0.8
/ 1.625293
inc
a d
kd
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Near-traped mode (Duclos and Clement, 2004)
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0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
1 1 0
1 2 0
1 3 0
1 4 0
1 5 0
0.0
Near-traped mode (Present, 2009)
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Perturbation parameter
0.3 0.5 0.9
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Perturbation parameter
- 2 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- 1 2
- 1 0
- 8
- 6
- 4
- 2
0
2
4
6
8
1 0
0.1 - 2 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0
- 1 2
- 1 0
- 8
- 6
- 4
- 2
0
2
4
6
8
1 0
0.3 - 2 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0
- 1 2
- 1 0
- 8
- 6
- 4
- 2
0
2
4
6
8
1 0
0.5
0 5 1 0 1 5 2 0 2 5 3 0
- 1 0
- 5
0
5
1 0
0 5 1 0 1 5 2 0 2 5 3 0
- 1 0
- 5
0
5
1 0
0.7 0.9
No trapped mode is found
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Horizontal force versus wave number
0 0.5 1 1.5 2
0
1
2
3
4
5
6
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Concluding remarks
A general-purpose program for solving the water wave problems with arbitrary number, size and various locations of circular cylinders was developed.
We have proposed a BIEM formulation by using degenerate kernels, null-field integral equation and Fourier series in companion with adaptive observer system.
Near trapped mode is observed in this study.
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The end
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