Longperiod 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 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 1

Typhon Tim 1994: Hualien Harbor, Taiwan H outside # 00 outside # 05 (# 00) inside # 22 inside #8 inside 0 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway T (sec) # 10 200 2

Port of Hualien 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 3

2 10 22 8 2 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 4

Typhoon Longwang, Oct. 2 nd 2005 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 5

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) 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 6

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 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 7

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Pairs of frequencies 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 13

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Frequency responses By Mild slope Approximation First-order Chamberlain & Porter (1995) Far field : analytical solution +radiation condition Near field: FEM Shallow Water Hydrodynamics, 12/19/2005 Trondheim, Norway 15

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Hybrid finite element method (Chen & Mei, 1974) (HFEM) Far Field Analytical Near Field Finite element 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 17

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Square harbor, Normal incidence 300 m by 300 m, depth h=20 m Effect of entrance (1) 60 m opening without protection (2) 30 m opening without protection (3) 30 m opening with protection 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 22

Random sea: TMA Spectrum 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 23

First-order average response 60 m, no protection 30 m with protection 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 24

Mean Linear spectrum 60 m, no protection 30 m with protection 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 25

Second-order Mean: setup/down 60 m 30 m, no protection 30 m, with protection 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 26

Nonlinear correction: long wave 60 m, no protection 30 m with protection 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 27

Mean Harbor Spectrum 60 m 30 m, no 30 m, protected 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 28

Qualitative comparison with field data 30 m, protected in out in 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 29

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 (4 G ram, 2. 8 G Hz), weeks 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 30

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 12/19/2005 Shallow Water Hydrodynamics, Trondheim, Norway 31