# Wave propagation through arrays of unevenly spaced vertical piles - PowerPoint PPT Presentation

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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

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Wave propagation through arrays of unevenly spaced vertical piles

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## Wave propagation through arrays of unevenly spaced vertical piles

Reporter : Yi-Jhou Lin

National Taiwan Ocean University

Department of Harbor and River Engineering

Date: February 06, 2009

Place: HR2 307

### Outlines

• Problem statement

• Numerical examples

• Concluding remarks

Original Problem

### Problem statement

Governing equation:

Separation variable :

where

Seabed boundary conditions :

Free-surface conditions :

where

Original Problem

### Decompose two parts

Free field

Original problem

Decompose two parts

Free field

Expansion

Degenerate kemel

For fundamental solution

Fourier series of boundary densities

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

Original Problem

### Near-traped mode (Duclos and Clement, 2004)

Near-traped mode (Present, 2009)

### Perturbation parameter

No trapped mode is found

### 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.