Tsunami Waveforms in South China Sea and Runup of Undular Bores

Transcription

1 SCSTW-7, Taichung, Nov Tsunami Waveforms in South China Sea and Runup of Undular Bores Xi Zhao Hua LIU MOE Key Lab of Hydrodynamics School of NAOCE, Shanghai Jiao Tong University

2 Contents 1 Introduction 2 Tsunami wave patterns in SCS 3 Runup of undular bores 4 Concluding remarks

3 2011 Japan Tohoku Tsunami Propagation of tsunami in Pacific Ocean Propagation of tsunami to China Coast

4 2011 Japan Tohoku Tsunami Tsunami wave recorded with DART Station H=1.12m, T/2=13min (from crest to trough), d=5822m

5 2011 Japan Tohoku Tsunami Contours of tsunami arrival time in China seas

6 2011 Japan Tohoku Tsunami (m) (m) DART_21401 Buoy USGS USSB DART_51407 Time (hr) Time (hr) Buoy USGS USSB

7 2011 Japan Tohoku Tsunami ( m ) Shenjiamen Gauge Model Time(hr) ( m ) Shipu Gauge Model Time(hr) ( m ) Shantou Gauge Model Time(hr) The maximum wave height of tsunami along China coast is about 0.6m.

8 Scenarios of local tsunami---ecs Computational domain and subduction zone

9 Surface elevation Scenarios of local tsunami---ecs

10 Scenarios of local tsunami---scs Computational domain and subduction zone in SCS

11 Scenarios of local tsunami---scs

12 Scenarios of local tsunami---scs 墾丁

13 Scenarios of local tsunami---scs 香港

14 Introduction East China Sea Wave patterns of the tsunami propagating over the continental shelf with a gentle slope?

15 Scenarios of local tsunami---csc Manila trench in SCS

16 South China Sea Introduction

17 Introduction Motivation of the study wave patterns of tsunami propagating on continental shelf with a gentle slope South China Sea and East China Sea Runup of undular bores

18 Contents 1 Introduction 2 Tsunami wave patterns in SCS 3 Runup of undular bores 4 Concluding remarks

19 Governing equations ~ w ~ ( V w~ ) 0 t ~ V 1 ~ ~ [ ~ 2 g V V w (1 )] 0 t 2 ~ V u~ w~ w b Tsunami wave patterns in SCS u b h h Solution of the Laplace equation for potential flow t Taylor operators Madsen, Bingham, Liu. JFM, 2002;Wang, Liu. IJNMF, 2005.

20 Tsunami wave patterns in SCS The slope of continental shelf in SCS changes from 1:300 to 1:800. The length of the continental shelf is about 200 km and 400 km, respectively.

21 Tsunami wave patterns in SCS South China Sea, Profile 1, M7.0

22 Tsunami wave patterns in SCS South China Sea, Profile 1, M9.0

23 Tsunami wave patterns in SCS South China Sea, Profile 2, M7.0

24 Tsunami wave patterns in SCS South China Sea, Profile 2, M9.0

25 Contents 1 Introduction 2 Tsunami wave patterns in SCS 3 Runup of undular bores 4 Concluding remarks

26 Runup of undular bores Runup of N-waves Amplification of wave height Runup of undular bores

27 Runup of N-waves Runup of N-waves η 3 2 3H m sech 2 [ k m ( x x 1 )]tanh[ k m ( x x 1 )] H m k m x 1 Case Case Case Case Case Case

28 Case 1 Runup of N-waves

29 Runup of N-waves Case 2 Case 3

30 Case 5 Runup of N-waves

31 Case 6 Runup of N-waves

32 Amplification of wave height Amplitude evolution of sinusoidal wave shoaling on a 1:4000 sloping beach

33 Amplification of wave height

34 Amplification of wave height Sinusoidal wave shoaling on a 1:4000 sloping beach by different models. Dash line: nonlinear shallow water equations, Dolid line: nonlinear and dispersive Boussinesq equations, Dot-dash line: linear model.

35 Runup of undular bores A simplified 1-D model for submarine earthquake ζ ( x', t) 2AC sech 2 ( Cx' ) tanh( Cx' )sin( πt / 2τ) Magnitude (Richter) W(km) C A Slip distance (m) τ (s)

36 Profile 1 Profile 2 Undular bores

37 Runup of undular bores A simplified model of the undular bores u 0 0 b0 η u0 b0 H0 Lu ε sin[ ku ( x x0)] ( 2 4 H 0 (-x n Lu x0)/ Lb 2 0 { x nlu x0) /( nlu ) H 0 2 nl u H 2 } x nl u L b x 0 x nl u H 0 /h 0 =0.02, L u =30h 0 H 0 /h 0 =0.01, L u =20h 0 nl u +L b =12L u nl u +L b =20L u

38 Runup of undular bores Maximum runup of every undulation. (L u =30h 0 ) The relative runup r/η changes only with the number of undulations. The relative wave height H 0 /h 0 and the lengths of the rest part of the long bores L b have no effect on r/η.

39 Runup of undular bores Maximum runup of every undulation. (L u =20h 0 ) The relative runup r/η increase with the decrease of the wave length of undulations.

40 Runup of undular bores The shoreline movement and energy budget during the runup process. (n=3, nl u +L b =12L u, H 0 /h 0 =0.02)

41 Runup of undular bores The shoreline movement and energy budget during the runup process. (n=7, nl u +L b =20L u, H 0 /h 0 =0.02) The undulations lead the shoreline to advance and recede significantly. The long bores don't bring maximum runup but brings the maximum potential energy of the tsunami waves to the coast.

42 Concluding remarks Considering the potential earthquake in Manila trench, much attention should be paid on impacts of the tsunami on China coast and other coastal countries along the South China Sea. Different wave patterns appear for tsunami propagating on a continental shelf with a gentle slope. Undular bore could appear in catostrophic tsunami wave in South China Sea.

43 Concluding remarks A simplified model of undular bores is proposed using summation of short sinusoidal components and a long attenuation component. The large advances of the shoreline are caused by the high undulations in front of the tsunami waves. However, the runup and rundown processes of the undulations don't lead to remarkable fluctuations of the energy transformation. The long bores don't bring maximum runup but brings the maximum potential energy of the tsunami wave to the coast.

44 SCSTW-7, Taichung, Nov Runup of Double Solitary Waves on Steep Slope Wei WU Hua LIU MOE Key Lab of Hydrodynamics School of NAOCE, Shanghai Jiao Tong University

45 Contents 1 Introduction 2 Experimental results 3 Numerical simulation 4 Concluding remarks

46 Introduction The run-up of single solitary wave: nonbreaking /breaking intensive experimental investigation empirical formulas for the maximum run-up height

47 Introduction H/d d(cm) H(cm) tan(β) Flume (m) Wave generation method Hall & Watts (1953) 0.05~ ~ ~10.1 1/11.4, 1/5.7, 1/3.7, 1/2.1, 1/ ramp trajectory Ippen & Kulin (1954) 0.20~ ~ ~9.6 1/43.5, 1/20, 1/ dam break Camfield & Street (1969) < ~76.2 <55.6 1/100, 1/50, 1/33.3, 1/ Tan-hyperbolic function Lee et al. (1982) 0.11, 0.19, , 7.68, , 40.45, Goring(1978) Papanicolaou & Raichelen (1987) 0.20~ ~ ~14.2 1/164, 1/106, 1/79, 1/63, 1/ Goring(1978) Synolakis (1987) 0.01~ ~ ~12.3 1/ Goring(1978) Yeh et al. (1989) 1/ dam break Grilli et.al. (1994) 0.10~ ~11.0 1/ Goring(1978) Li (2000) 0.04~0.5 7~ ~13.7 1/19.85, 1/ Goring(1978) Li (2001) 0.04~ ~ ~15.2 1/ CERC Goring(1978) Jensen et al. (2003) 0.12, 0.53, 0.335, , 20 1/ SW like impuls O Donoghue et al. (2006) 1/ dam break Yu-Hsuan Chang et al. (2008) 0.05~ ~325 3~49 1/60, 1/40, 1/ Goring(1978) & ramp trajectory

48 Introduction Pedersen & Gjevik(1983): shallow water equations Zelt & Raichlen(1990): shallow water equations Kim Liu & Ligett(1983): BIEM Carrier & Greenpan(1958, JFM): C-G transform method Synolakis(1987, JFM): runup, solitary wave Tadepalli & Synolakis(1994, JFM): runup Stefanakis & Dias(2011, JFM): resonant runup Zhao, Wang, Liu(2012, PoF): solitary wave, runup

49 Introduction Grue et al.(2008), Madsen et al.( 2008) : undular bores appear in tsunami propagation in offshore waters. The undular bores can be modeling as a combination of several solitary waves with different wave heights and different separation distance between the successive wave peaks. Lo, Park and Liu (2013): the run-up and back-wash processes of the double solitary waves consisting of two identical solitary waves, flume experiments. The beach slope s=1/5~ 1/20 and H/d=0.1~0.3.

50 Introduction Topography profile from Shanghai to the Okinawa Trench in East China Sea slope=1:3000

51 Introduction

52 Introduction Lo, Park and Liu(2013) s Double Solitary Waves : two successive solitary waves, separated by a specified separation time, are generated by linearly combining the wave-maker trajectories of two individual solitary. Xuan, Wu and Liu(2013): Double Solitary Waves with unequal individual wave height

53 Introduction Motivation of the study Runup of individual wave of the double solitary waves Velocity field and energy budge of the double solitary waves during runup on a vertical wall or a slope

54 Experimental approach Wave generation method solitary wave of large amplitude Runup of single solitary wave Runup of double solitary waves

55 Experimental approach Goring method _ d u, t u, t dt _ c, t d, t KdV H kd t tanh k ct The 3 rd order solution t th th + th th sh th sh th k

56 Experimental approach Modified Goring method (Malek-Mohammadi & Testik) d u, t u1, t dt t cu, t c d, u t d dt d 2 d _ u1 g d æ ( ) = gçd + h 2 è öæ 1+ h ö ç øè d ø Comparison of displacement and velocity of wavemaker (α=0.5)

57 Experimental approach Input signal of wavemaker: The 1 st order solitary wave

58 Experimental approach Input signal for wavemaker: the 3 rd order solitary wave

59 Experimental approach Time series of surface elevation for a solitary wave (α=0.5, KdV) Time series of surface elevation for a solitary wave (α=0.5, 3 rd theory)

60 Experimental approach Generation of two solitary waves x, sh 1 th th sh th 2SH 1 TH ( TH SH TH ) h α 1 & α relative wave sh sech k x X 1 th----tanh k x X 1 SH TH sech k x X T tanh k x X T

61 Experimental approach Vertical wall reflection, H 1 /d=0.133, H 2 /d=0.133, εt=1.0

62 Experimental approach Vertical wall reflection, H 1 /d=0.133, H 2 /d=0.133, εt=0.8

63 Experimental approach Vertical wall reflection, H 1 /d=0.133, H 2 /d=0.133, εt=0.6

64 Experimental approach Vertical wall reflection, H 1 /d=0.133, H 2 /d=0.133, εt=0.4

65 Experimental approach Vertical wall reflection, H 1 /d=0.1, H 2 /d=0.233, εt=1.0

66 Experimental approach Vertical wall reflection, H 1 /d=0.1, H 2 /d=0.233, εt=0.8

67 Experimental approach Vertical wall reflection, H 1 /d=0.1, H 2 /d=0.233, εt=0.6

68 Experimental approach Vertical wall reflection, H 1 /d=0.1, H 2 /d=0.233, εt=0.4

69 Experimental approach Vertical wall reflection, H 1 /d=0.233, H 2 /d=0.1, εt=0.4

70 Experimental approach Vertical wall reflection, H 1 /d=0.233, H 2 /d=0.1, εt=0.6

71 Experimental approach Vertical wall reflection, H 1 /d=0.233, H 2 /d=0.1, εt=0.8

72 Experimental approach Vertical wall reflection, H 1 /d=0.233, H 2 /d=0.1, εt=1.0

73 Numerical Wave Flume Guo, Wang, Liu(2014, JWWEN): RANS+RNG k-e model+vof

74 Results and discussion x = 4.5m H 1 /d = H 2 /d = experiment result x = 8.5m simulation result x = 12.5m x = 16.5m x =20.5m x = 24.5m x = 28.5m 0.05 x = 32.5m The Moving Shoreline t(g/d) 1/2 等波高孤立波的直墙爬高

75 Results and discussion H 1 /d = H 2 /d = x = 4.5m experiment result x = 8.5m simulation result x = 12.5m x = 16.5m x =20.5m x = 24.5m x = 28.5m The Moving Shoreline t(g/d) 1/2 等波高孤立波的直墙爬高 x = 32.5m

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77 Results and discussion L ( L / d) / ( H1/ H2) R H 2 2 R H , The relationship between the run-up amplification coefficient and the similarity factor for the double solitary wave with identical individual wave height

78 Results and discussion Reflection Wave Reflection Wave Incident Wave Incident Wave Reflection Wave Reflection Wave Incident Wave Incident Wave Waveforms evolution and moving shoreline of the double solitary waves (L+S pattern): vertical wall

79 Results and discussion Reflection Wave Reflection Wave Incident Wave Incident Wave Incident Wave Reflection Wave Incident Wave Reflection Wave Waveforms evolution and moving shoreline of the double solitary waves (L+S pattern): β=45 o

80 Results and discussion The relationship between the run-up amplification coefficient and the similarity factor for the double solitary waves (L+S pattern)

81 Results and discussion Incident Wave Reflection Wave Incident Wave Reflection Wave Incident Wave Reflection Wave Incident Wave Reflection Wave Waveforms evolution and moving shoreline of the double solitary waves (S+L pattern): vertical wall

82 Results and discussion Reflection Wave Incident Wave Incident Wave Reflection Wave Incident Wave Reflection Wave Incident Wave Reflection Wave Waveforms evolution and moving shoreline of the double solitary waves (S+L pattern): β=45 o

83 Results and discussion The relationship between the run-up amplification coefficient and the similarity factor for the double solitary waves (S+L pattern)

84 Results and discussion 1.0 R 1 R 2 Kinetic energy Potential energy total energy E/E n t(g/d) 1/2 Kinetic energy Potential energy R R 2 1 total energy E/E n t(g/d) 1/2 1.0 Kinetic energy R 1 R 2 Potential energy total energy E/E n t(g/d) 1/2 Zhao, Wang, Liu (2012, PoF): energy budge, single solitary wave, slope beach

85 Concluding Remarks For the runup of the double solitary waves with equal wave height, the runup amplification coefficient is less than 1.0 for the case of as the small distance between two wave crests. For the case of the double solitary waves, which consists of one smaller wave followed by a larger wave at the initial time (S+L pattern), the runup amplification is less than 1.0 for the cases of smaller values of the similarity factor χ. It is found that the solitary wave with larger amplitude overtakes the first smaller wave before the runup begins.

86 Concluding Remarks If the factor χ is larger than a threshold value, which represents the cases that the leading smaller wave runup on the slope at first, the runup amplification of the second wave with larger amplitude is larger than that of the first wave. There are three peaks in the time series of the total potential energy of the wave field during the period of the runup of the double solitary waves against a vertical wall.

87 Thank You!