Long-period Harbor Oscillations due to Short Random Waves

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Long-period Harbor Oscillations due to Short Random Waves

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Long-period Harbor Oscillations due to Short Random Waves

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Long-period Harbor Oscillations due to Short Random Waves

Meng-Yi Chen & Chiang C. Mei

Massachusetts Institute of Technology

Shallow Water Hydrodynamics, Trondheim, Norway

H

outside

# 00

outside

# 05

(# 00)

inside

# 22

inside

# 8

inside

# 10

0

T (sec)

200

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

2

10

22

8

2

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

- Harbor Oscillations
- Linear theory

Miles & Munk (1961), Miles( 1971), Lee(1971),

Unluata & Mei (1973), (1978) , Carrier,Shaw & Miyata(1971)

- Nonlinear approximation -- narrow-banded
Bowers(1977), Agnon & Mei (1989), Wu & Liu (1990)

- Nonlinear approximation -- narrow-banded

Shallow Water Hydrodynamics, Trondheim, Norway

- Sclavounos (1992)
-Stochastic theory

-Simple progressive and standing wave in deep water

-Incident waves: stationary, Gaussian

-Higher order spectrum depends on

first, second, and third-order

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Pairs of frequencies

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Frequency responses By Mild slope Approximation

First-order

Chamberlain & Porter (1995)

Far field : analytical solution +radiation condition

Near field: FEM

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Far Field

Analytical

Near Field

Finite element

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

Effect of entrance(1) 60 m opening withoutprotection

(2) 30 m opening withoutprotection

(3) 30 m openingwithprotection

Shallow Water Hydrodynamics, Trondheim, Norway

Shallow Water Hydrodynamics, Trondheim, Norway

60m, no protection

30m, no protection

30m with protection

Shallow Water Hydrodynamics, Trondheim, Norway

60m, no protection

30m, no protection

30m with protection

Shallow Water Hydrodynamics, Trondheim, Norway

60m

30m, no protection

30m, with protection

Shallow Water Hydrodynamics, Trondheim, Norway

60m, no protection

30m, no protection

30m with protection

Shallow Water Hydrodynamics, Trondheim, Norway

60m

30m,no

30m, protected

Shallow Water Hydrodynamics, Trondheim, Norway

30m, protected

out

in

out

in

Shallow Water Hydrodynamics, Trondheim, Norway

- For 2-nd order problem must be solved for a many pairs of frequencies by FEM
- Large sparse matrix for each pair
-- for variable depth: modes are coupled

--10620 pairs, each pair need around 15 minutes, at least 100 days for ONE single computer,

--20-25 parallel computer (4G ram, 2.8G Hz), weeks

Shallow Water Hydrodynamics, Trondheim, Norway

- Stochastic theory for long-period harbor resonance by a broad-banded sea

-Long-wave part of response spectrum is dominated by second-order correction, not first or third-order

-Mild-slope equation for second order in wave steepness is sufficient

-High-frequency part of response spectrum is dominated by first-order wave

-Extendable to Slow drift of floating structures

Shallow Water Hydrodynamics, Trondheim, Norway