Wave-induced oscillations in harbors of arbitrary
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Transcript of Wave-induced oscillations in harbors of arbitrary
BEM Final report PP.1
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
Jan. 7, 2010 BEM Final report PP.3
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
Jan. 7, 2010 BEM Final report PP.5
Formulation
Weber’s solution:
Modified Weber’s solution:
rearrange
T u U t
discrete form obtain
Wave function inside the Harbor (Region II)
Jan. 7, 2010 BEM Final report PP.6
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
Jan. 7, 2010 BEM Final report PP.9
Numerical examples
• Circular harbor with a 10o and a 60o opening
• Rectangular harbor
• An example of a harbor with complicated shape
BEM Final report PP.14
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