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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. 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

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

  2. 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

  3. Port of Hualien Shallow Water Hydrodynamics, Trondheim, Norway

  4. 2 10 22 8 2 Shallow Water Hydrodynamics, Trondheim, Norway

  5. Typhoon Longwang, Oct. 2nd 2005 Shallow 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) Shallow 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 Shallow Water Hydrodynamics, Trondheim, Norway

  8. Shallow Water Hydrodynamics, Trondheim, Norway

  9. Shallow Water Hydrodynamics, Trondheim, Norway

  10. Shallow Water Hydrodynamics, Trondheim, Norway

  11. Shallow Water Hydrodynamics, Trondheim, Norway

  12. Shallow Water Hydrodynamics, Trondheim, Norway

  13. Pairs of frequencies Shallow Water Hydrodynamics, Trondheim, Norway

  14. Shallow 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 Shallow Water Hydrodynamics, Trondheim, Norway

  16. Shallow Water Hydrodynamics, Trondheim, Norway

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

  18. Shallow Water Hydrodynamics, Trondheim, Norway

  19. Shallow Water Hydrodynamics, Trondheim, Norway

  20. Shallow Water Hydrodynamics, Trondheim, Norway

  21. Shallow Water Hydrodynamics, Trondheim, Norway

  22. 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

  23. Random sea: TMA Spectrum Shallow Water Hydrodynamics, Trondheim, Norway

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

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

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

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

  28. Mean Harbor Spectrum 60m 30m,no 30m, protected Shallow Water Hydrodynamics, Trondheim, Norway

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

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