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Long-period Harbor Oscillations due to Short Random Waves. Meng-Yi Chen & Chiang C. Mei Massachusetts Institute of Technology. Typhon Tim 1994 : Hualien Harbor,Taiwan. H. outside. # 00. outside. # 05. (# 00). inside. # 22. inside. # 8. inside. # 10. 0. T (sec). 200.

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Long period harbor oscillations due to short random waves

Long-period Harbor Oscillations due to Short Random Waves

Meng-Yi Chen & Chiang C. Mei

Massachusetts Institute of Technology

Shallow Water Hydrodynamics, Trondheim, Norway


Typhon tim 1994 hualien harbor taiwan
Typhon Tim 1994: Hualien Harbor,Taiwan

H

outside

# 00

outside

# 05

(# 00)

inside

# 22

inside

# 8

inside

# 10

0

T (sec)

200

Shallow Water Hydrodynamics, Trondheim, Norway


Port of hualien
Port of Hualien

Shallow Water Hydrodynamics, Trondheim, Norway


Long period harbor oscillations due to short random waves

2

10

22

8

2

Shallow Water Hydrodynamics, Trondheim, Norway


Typhoon longwang oct 2 nd 2005
Typhoon Longwang, Oct. 2nd 2005

Shallow Water Hydrodynamics, Trondheim, Norway


Past works
Past Works

  • 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)

Shallow Water Hydrodynamics, Trondheim, Norway


Standing waves near a cliff random sea
Standing waves near a cliff-Random sea

  • 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







Long period harbor oscillations due to short random waves

Pairs of frequencies

Shallow Water Hydrodynamics, Trondheim, Norway



Long period harbor oscillations due to short random waves

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



Hybrid finite element method chen mei 1974 hfem
Hybrid finite element method (Chen & Mei,1974)(HFEM)

Far Field

Analytical

Near Field

Finite element

Shallow Water Hydrodynamics, Trondheim, Norway






Square harbor normal incidence 300m by 300 m depth h 20m
Square harbor, Normal incidence 300m by 300 m, depth h=20m

Effect of entrance(1) 60 m opening withoutprotection

(2) 30 m opening withoutprotection

(3) 30 m openingwithprotection

Shallow Water Hydrodynamics, Trondheim, Norway


Random sea tma spectrum
Random sea: TMA Spectrum

Shallow Water Hydrodynamics, Trondheim, Norway


First order average response
First-order average response

60m, no protection

30m, no protection

30m with protection

Shallow Water Hydrodynamics, Trondheim, Norway


Mean linear spectrum
Mean Linear spectrum

60m, no protection

30m, no protection

30m with protection

Shallow Water Hydrodynamics, Trondheim, Norway


Second order mean setup down
Second-order Mean: setup/down

60m

30m, no protection

30m, with protection

Shallow Water Hydrodynamics, Trondheim, Norway


Nonlinear correction long wave
Nonlinear correction: long wave

60m, no protection

30m, no protection

30m with protection

Shallow Water Hydrodynamics, Trondheim, Norway


Mean harbor spectrum
Mean Harbor Spectrum

60m

30m,no

30m, protected

Shallow Water Hydrodynamics, Trondheim, Norway


Qualitative comparison with field data
Qualitative comparison with field data

30m, protected

out

in

out

in

Shallow Water Hydrodynamics, Trondheim, Norway


Numerical aspects
Numerical Aspects

  • 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


Summary
Summary

- 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