1. 12/19/2005Shallow Water Hydrodynamics, Trondheim, Norway 1 Long-period Harbor Oscillations due to Short Random Waves Meng-Yi Chen & Chiang C. Mei Massachusetts Institute of Technology

2. 12/19/2005Shallow Water Hydrodynamics, Trondheim, Norway 2 Typhon Tim 1994: Hualien Harbor,Taiwan (# 00) # 8# 8# 8# 8 # 00 # 00 # 05 # 05 # 22 # 22 # 10 # 10 outside inside outside inside T (sec) 0200 H inside

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

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

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

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

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

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

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

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

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

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

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

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

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

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

28. 12/19/2005Shallow Water Hydrodynamics, Trondheim, Norway 28 Mean Harbor Spectrum 60m30m,no 30m, protected

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

30. 12/19/2005Shallow Water Hydrodynamics, Trondheim, Norway 30 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

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