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Wave-induced oscillations in harbors of arbitrary

Reporter: Chine-Feng WuAdvisor: Jeng-Tzong ChenDate: Jan. 07, 2010

Jiin-Jen Lee

J. Fluid. Mech., vol. 45, no. 2, pp. 375-394

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Engineering problems

California: Santa Catalina Island

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Water wave

.),,(,0);,,(2 Dzyxtzyx

1( , , , ) ( , ) ( ) i tx y z t f x y Z z e

i

cosh ( )( )

coshiigA k z h

Z zkh

Governing equation:

Separation variable :

).,(,0 yxhzn

where

Seabed boundary conditions :

0

1, , , i t

iz

x y t A f x y eg t

Velocity potential :

cosh ( )1( , , ) ,

coshi tigA k z h

x y t f x y ei kh

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Continuity condition：

1 21 2 and ,

f ff f

n n

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Formulation

Weber’s solution：

Modified Weber’s solution：

rearrange

T u U t

discrete form obtain

Wave function inside the Harbor (Region II)

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1X X P

2 ni G G

2

2

X , 1,2,...,

P , 1,2,...,

i

j

f x i N

f x j Nn

1

P C, for 1, 2,..., , 1, 2,..., .p

ij j mj

C U j p i N

Can be expressed as a function of the unknown normal derivative of f2 at the harbor entrance

1,2,...,i N

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Wave function inside the Harbor (Region I)

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Numerical examples

• Circular harbor with a 10o and a 60o opening

• Rectangular harbor

• An example of a harbor with complicated shape

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Circular harbor with a 10o opening

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Circular harbor with a 60o opening

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Rectangular harbor

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Complicated shape

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Thanks for your kind attentionsYou can get more information from our website.

http://msvlab.hre.ntou.edu.tw/

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