1. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Measurement of Infragravity Edge Waves on the East Coast of Taiwan using a Single Instrument Guan-Yu Chen, Hsiao-Ching Chien Institute of Applied Marine Physics and Undersea Technology, National Sun Yat-Sen University Hsiang-Mao Tseng Institute of Harbor and Marine Technology

2. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The instantaneous surface elevation of the edge wave

3. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The importance of edge wave is first proposed when Crescentic Sandbar were noticed 邊緣波與沙嘴 / 新月型沙洲的形成有關

4. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Formation Of Cusps By Edge Waves

5. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins For most harbors, the harbor entrance is facing the open sea

6. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Examples: harbor entrance is facing the open sea

7. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Examples: harbor entrance is facing the open sea

8. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Instead of facing the sea,the Hua-Lien harbor is along the long straight east coast of Taiwan This specific layout of Hua-Lien harbor makes the basin vulnerable to the influence of edge waves.

9. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins When a typhoon moved northward from the southeast, the wave condition inside the Hua-Lien Harbor can be very dangerous Even when the center is far away

10. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins

12. Series of offshore detached breakwaters constructed outside the harbor, resulting in delaying the resonance inside for more than one hour

13. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 侷限波與滲漏波

14. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins

17. Bad News Infragravity edge wave has never been observed in the east coast of Taiwan. identifying the existence of edge waves is very helpful in designing countermeasures

18. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The locations of three stations N (north), S (south) and M (main) near the entrance of Hua- Lien Harbor

19. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The traditional approach to edge wave measurement requires some twenty instruments

20. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Scale Analysis Infragravity velocity component is of order 0.2m/s or smaller Advection term can be neglected The Earth rotates at about 10^-4/sec Coriolis effect can be neglected

21. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Scale Analysis (2) Kinematic viscosity for water is less than 1 m^2/s Time scale for Infragravity motion is 20-500 sec The Earth rotates at about 10^-4/sec Length scale for Infragravity edge wave is which is of order 1000m. Viscosity can be neglected.

22. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Scale Analysis (3) For water depth around 20 m the friction in the vertical direction is also negligible for infragravity waves (1) (2) 海洋波動研究室

23. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins If waves are generated far away along the coast, their direction is easy to determine Although reflection of the shoreline is possible, these waves are basically progressive.

24. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins If waves are generated far away along the coast, these waves are basically progressive. Specific Fourier components of dynamic pressure and y-velocity are both proportional to exp(iky-i  t). The p-v relation is derived as (3) 海洋波動研究室

25. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 1. For an infragravity leaky wave, the phase velocity is exactly the shallow water celerity 2. For an edge wave where s is the constant bottom slope, T is the wave period and the integer n is the mode number 海洋波動研究室

26. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Stations N and M are close to the harbor entrance where a progressive wave could be reflected by the breakwaters and form standing waves

27. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins If waves are generated far away along the coast, their direction is easy to determine Although reflection of the shoreline is possible, these waves are basically progressive.

28. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Typhoons in 2005 are too close to Hua- Lien and hence the direction of the typhoon waves cannot be determined

29. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Track of Typhoon Kaemi is in the south of Hua-Lien; the edge wave feature is significant even when the typhoon is 500 km away from Hua-Lien

30. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Typhoon Kaemi (23-26 July, 2006) affected the Hua-Lien coast from five o’clock of July 23rd.

31. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The time series of pressure, eastward and northward flow measured at station S

32. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The IMF's of the pressure time series recorded at 6 AM of July 23rd

33. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 1. For an infragravity leaky wave, the phase velocity is exactly the shallow water celerity 2. For an edge wave where s is the constant bottom slope, T is the wave period and the integer n is the mode number 海洋波動研究室

34. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The spectrum inside the harbor during Typhoon Tim (July, 1994), is concentrated in two period ranges: 70-120 sec and 120-190 sec.

35. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 05:00, 23 July

36. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins The observed pressure is proportional to the longshore velocity. The proportionality ratio is close to the theoretical relation with n=0 which corresponds to Stokes edge waves. The theoretical lines for the first three edge wave modes are drawn together to show the existence of a Stokes edge wave.

37. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 06:00, 23 July

38. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins To exclude the possibility of mistakenly interpreting a leaky wave as an edge wave, the maximum flow, instead of the longshore component of the infragravity wave, is used, with the shallow water celerity being used in computing the theoretical slope When the wave started to affect the Hua- Lien coast, the edge wave features are significant.

39. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 19:00, 24 July

40. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 19:30, 24 July

41. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins When the typhoon is close to the land, the p-u relation becomes much more complicated. Some cases show leaky wave features The wave energy is distributed in several modes.

42. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 05:00, 25 July

43. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 12:00, 25 July

44. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins 09:00, 25 July

45. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins in the late stages of Typhoon Kaemi on 25 July show clear Stokes edge wave features again Lower mode edge waves propagate slower than plane leaky waves and are highly dispersive

46. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Summary The present p-v approach requires only a single instrument and hence is a much easier and cheaper method for measuring edge waves. By contrast, the traditional frequency- wavenumber approach needs 20 instruments.

47. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Discussion The present approach implicitly assumes that at each frequency range the edge wave energy is concentrated in just one mode. For some engineering problems such as beach erosion and tsunami incidents, identifying the existence of edge waves is very helpful in designing countermeasures.

48. International Symposium on Sediment Transport and Sedimentation on Asian Continental Margins Thank you for your attention 歡迎提問